Maria Colonna Laboratori Nazionali del Sud (Catania)

Nuclear Matter and Nuclear Dynamics Nuclear Matter and Nuclear Dynamics

XII Convegno su Problemi di Fisica Nucleare TeoricaCortona 8-10 Ottobre 2008

The EOS of symmetric and neutron matter from many-body theoriesThe EOS of symmetric and neutron matter from many-body theoriesthe energy functional is calculated from the bare nucleon-nucleon interaction

Information on EInformation on Esymsym behavior from Heavy Ion Collisions behavior from Heavy Ion Collisions Transport theories

High density EOS High density EOS implications on the structure of neutron starsimplications on the structure of neutron stars

Transition to the QGP Transition to the QGP Role of isospin

Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations

BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction

TBF consistent with the underlying two-nucleon One Boson Exchange potential

Results for EOS and symmetry energy

Li Lombardo Schulze Zuo PRC 2008

Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF

Constraints on pressure from nuclear flow data analysis

The overall effect of the same TBF on the EOS can be different according to the two-body force adopted

Stiffer EOS with TBF

EOS symm matterPhenomenological Urbana type TBF

Bonn B

v18

Similar EOS

BaldoShaban PLB661(08)

Li Lombardo Schulze Zuo PRC77(08)

EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter

Dirac-BruecknerRMFDensity-Dependent couplings

Symmetric Matter | Symmetry Energy | Neutron Matter

DD-F

NLρ

NLρδ

Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802

Slope at normal densityIsospin transport at Fermi energies

BOB

Urbana

AFDMC

asy-soft

asy-stiff

Effective parameterizationsof symmetry energy

Transport codesNuclear Dynamics

Astrophysical problems

SGandolfi et al PRL98(2007)102503

Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs

Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems

Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)

Nuclear DynamicsNuclear Dynamics

High density behavior Neutron stars

Transport equations

Phys Rep 389 (2004)

PhysRep410(2005)335

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
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• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

The EOS of symmetric and neutron matter from many-body theoriesThe EOS of symmetric and neutron matter from many-body theoriesthe energy functional is calculated from the bare nucleon-nucleon interaction

Information on EInformation on Esymsym behavior from Heavy Ion Collisions behavior from Heavy Ion Collisions Transport theories

High density EOS High density EOS implications on the structure of neutron starsimplications on the structure of neutron stars

Transition to the QGP Transition to the QGP Role of isospin

Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations

BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction

TBF consistent with the underlying two-nucleon One Boson Exchange potential

Results for EOS and symmetry energy

Li Lombardo Schulze Zuo PRC 2008

Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF

Constraints on pressure from nuclear flow data analysis

The overall effect of the same TBF on the EOS can be different according to the two-body force adopted

Stiffer EOS with TBF

EOS symm matterPhenomenological Urbana type TBF

Bonn B

v18

Similar EOS

BaldoShaban PLB661(08)

Li Lombardo Schulze Zuo PRC77(08)

EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter

Dirac-BruecknerRMFDensity-Dependent couplings

Symmetric Matter | Symmetry Energy | Neutron Matter

DD-F

NLρ

NLρδ

Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802

Slope at normal densityIsospin transport at Fermi energies

BOB

Urbana

AFDMC

asy-soft

asy-stiff

Effective parameterizationsof symmetry energy

Transport codesNuclear Dynamics

Astrophysical problems

SGandolfi et al PRL98(2007)102503

Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs

Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems

Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)

Nuclear DynamicsNuclear Dynamics

High density behavior Neutron stars

Transport equations

Phys Rep 389 (2004)

PhysRep410(2005)335

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations

BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction

TBF consistent with the underlying two-nucleon One Boson Exchange potential

Results for EOS and symmetry energy

Li Lombardo Schulze Zuo PRC 2008

Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF

Constraints on pressure from nuclear flow data analysis

The overall effect of the same TBF on the EOS can be different according to the two-body force adopted

Stiffer EOS with TBF

EOS symm matterPhenomenological Urbana type TBF

Bonn B

v18

Similar EOS

BaldoShaban PLB661(08)

Li Lombardo Schulze Zuo PRC77(08)

EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter

Dirac-BruecknerRMFDensity-Dependent couplings

Symmetric Matter | Symmetry Energy | Neutron Matter

DD-F

NLρ

NLρδ

Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802

Slope at normal densityIsospin transport at Fermi energies

BOB

Urbana

AFDMC

asy-soft

asy-stiff

Effective parameterizationsof symmetry energy

Transport codesNuclear Dynamics

Astrophysical problems

SGandolfi et al PRL98(2007)102503

Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs

Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems

Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)

Nuclear DynamicsNuclear Dynamics

High density behavior Neutron stars

Transport equations

Phys Rep 389 (2004)

PhysRep410(2005)335

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter

Dirac-BruecknerRMFDensity-Dependent couplings

Symmetric Matter | Symmetry Energy | Neutron Matter

DD-F

NLρ

NLρδ

Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802

Slope at normal densityIsospin transport at Fermi energies

BOB

Urbana

AFDMC

asy-soft

asy-stiff

Effective parameterizationsof symmetry energy

Transport codesNuclear Dynamics

Astrophysical problems

SGandolfi et al PRL98(2007)102503

Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs

Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems

Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)

Nuclear DynamicsNuclear Dynamics

High density behavior Neutron stars

Transport equations

Phys Rep 389 (2004)

PhysRep410(2005)335

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs

Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems

Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)

Nuclear DynamicsNuclear Dynamics

High density behavior Neutron stars

Transport equations

Phys Rep 389 (2004)

PhysRep410(2005)335

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t

fWWfdtdf

Ensemble average

Langevin randomwalk in phase-space

Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t

Boltzmann

)()()()()( tprKfKprffhprft

LangevinVlasov

Vlasov Boltzmann Langevin

)(2

)(2

fUm

pfhi

i

Vlasov mean field

Boltzmann average collision term

( ) ( ) NNf i f i

dp p E Ed

3 3 32 1 2

2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h

Loss term

D(pprsquor)

SMF model fluctuations projected onto ordinary space density fluctuations δρ

Fluctuation variance σ2f = ltδfδfgt

D(pprsquor) w

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Collective excitations

Charge equilibration

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions

Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)

Zrel = zn ndash zpXrel = xn - xp

T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel

DassoGallardoLanzaSofia NPA801(2008)129

(neutron skin)Larger amplitude due to nuclear field

one-phonon

two-phonon

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

212

2

1

1210 RR

ZN

ZN

AZZD

D(t) bremss dipole radiation CN stat GDRInitial Dipole

Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

BMartin et al PLB 664 (2008) 47

Experimental evidence of the extra-yield LNS data

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Isospin gradients Pre-equilibrium dipole emission

SPIRALS rarr Collective Oscillations

22

3

2

)(3

2

DA

NZEc

edEdP

Bremsstrahlung Quantitative estimations

VBaran DMBrink MColonna MDi Toro PRL87(2001)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

1)(

1)()()(

TDHF CSimenel PhChomaz Gde France

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength arXiv08074118

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

b=8f

m

ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV

SMF - transport modelcalculations

experimental data (B Tsang et al PRL 92 (2004) )

Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and

Imbalance ratios

x = β = (N-Z)A

τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation

M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn

Kinetic energy loss

L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn

Time

JRizzo et al NPA806 (2008) 79

Several isoscalarinteractions

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Unstable dynamics

Liquid-gas phase transitionFragmentation in exotic systems

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm

Sn124 + Sn124 EA = 50 MeVA

Central collisions

Ni + Au EA = 45 MeVA

(fluctuations projected on ordinary space)

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Isospin-dependent liquid-gas phase transition

Isospin distillation the liquid phase is more symmetric than the gas phase

β = 02

β = 01

Non-homogeneous density

asy-stiff - - -asy-soft

Density gradients derivative of Esym

asy-soft

asy-stiff

Spinodal decomposition in a box (quasi-analytical calculations)

β = 02

β = 01

NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo

Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606

arXiv07073416

arXiv07073416Cluster density

asy-soft

asy-stiff

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF TLFneckemittednucleons

ρ1 lt ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007

Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics

LNS data ndash CHIMERA coll

VrelVViola (IMFPLF)

(IMFTLF)

JRizzo et al NPA806 (2008) 79

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Reactions at intermediate energies

Information on high density behaviorof Esym

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

scattering nuclear interaction from meson exchange main channels (plus correlations)

Isoscalar Isovector

Attraction amp Repulsion Saturation

OBE

JggVmW

ggΦm

ψψˆˆ

ρψψˆ

2

S2

Scalar Vector Scalar Vector

VVmWWΦmΦΦΦgMVgiL ˆˆ

21ˆˆ

41ˆˆˆ

21ˆˆ 222

Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach

Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)

Relativistic structure alsoin isospin space

Esym= kin + (vector) ndash ( scalar)

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

RBUU transport equation

Collision term

collprr IfUfmp

tf

Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip

Non-relativistic Boltzmann-Nordheim-Vlasov

drift mean fieldisi

iii

Mm

kk

F

ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term

Self-Energy contributions to the inelastic channels

Vector field

Scalar field

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Au+Au central π and K yield ratios vs beam energy

Pions large effects at lower energies

Kaons~15 difference betweenDDF and NLρδ

Inclusive multiplicities

132Sn+124Sn

GFerini et alPRL 97 (2006) 202301

NL

NLρ

NLρδ BF

Fsym E

MffEkE

2

2

2

21

61 2

m

gf

RMF Symmetry Energy the δ -mechanism

Effects on particle production

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Collective (elliptic) flowCollective (elliptic) flow

Out-of-plane

yyx

yxt pp

pppy 22

22

2 )(V

)(V)(V)(V n2

p2

n-p2 ttt ppp

1 lt V2 lt +1

= 1 full outV2 = 0 spherical = + 1 full in

Differential flows

)(1)(1

)(1)(

pn

pyvZN

pyv

i

tiitalDifferenti

B-A Li et al PRL2002

High pT selection

mnltmp larger neutron squeeze out at mid-rapidity

Measure of effective masses in high density ndash highly asymmetric matter

VGiordano Diploma Thesis

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Neutron stars as laboratories for the study of dense matter

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm

hadron-to-quark transition

Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the

maximum mass to values similar to data

2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram

PengLiLombardo PRC77 (08) 065807

CDDM model

)()(

()()

)()(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

density and charge conservation

Gibbs equilibrium condition +

Density dependent quark massBonn B

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS

NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18

Serious problems for our understanding of the EOS if large masses (about 2) are observed

Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS

Hybrid starsHybrid stars

Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022

2

13

2

4

)21)(41)(1(

rdrdm

rm

mrPP

rm

drdP

Tolmann-Oppenheimer-Volkov equation

Schulze et al

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

MBaldo amp C Maieron PRC 77 015801 (2008)

Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter

QMC

EOS of low-density neutron matter EOS of low-density neutron matter

- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)

- The dominant correlation comes from the Pauli operator

- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible

- Scattering length and effective range determine completely the G-matrix

- Variational calculations are slightly above BBG Good agreement with QMC

In this density range one can get the ldquoexactrdquo neutron matter EOS

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

GasLiquid

Density

Big Bang Te

mpe

ratu

re

20

200

M

eV Plasma of

Quarks and

Gluons

Collisions

HeavyIon

1 nuclei 5

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

Isospin

Mixed PhaseIn terrestrialLabs

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

AGeVUU 1238238 fmb 7

Exotic matter over 10 fmc

In a CM cell

Mixed phase in terrestrial labs

TGaitanos RBUU calculations

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Testing deconfinement with RIBrsquos

Hadron-RMF

trans onset of the mixed phase rarr decreases with asymmetrySignatures

DragoLavagno Di Toro NPA775(2006)102-126

Trajectories of 132Sn+124Sn semicentral

QH

QB

HBB

333 )1(

)1(

NLρ

NLρδGM3

B14 =150 MeV

1 AGeV 300 AMeV

Neutron migration to the quark clusters (instead of a fast emission)

Quark-Bag model

(two flavors)

Symmetry energies

symmetricneutron

- Large variation for hadron EOS - Quark matter Fermi contribution only

Crucial role of symmetry energy in quark matter

M Di Toro

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

QGP dynamics

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

xy z

px

py

RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with

Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after

the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV

(according to hydrodynamical calculations)(according to hydrodynamical calculations)

But finite mean free path But finite mean free path call for a transport approachcall for a transport approach

Quark dynamics in the QGP phaseQuark dynamics in the QGP phase

- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence

22

22

xyxy

x

22

22

2 2cosyx

yx

pppp

v

nn

TT

ndpdN

ddpdN )cos(v21

Perform a Fourier expansion of the momentum space particle distributions

Parton cascade

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue

s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling

Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out

Quantum mechanism s gt 115

λ151

ps

131

T

tE

No freeze-outs=14

vv22(p(pTT) as a measure of ) as a measure of ss

Ferini et al 0805 4814 [nucl-th]

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Ab initio partonic transport code p-p collisions

hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model

Calculations for nuclear matter inside a box

Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions

Total cross sectionPredictions for rapidity distributions at LHC

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Conclusions and Perspectives Conclusions and Perspectives

Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503

Still large uncertainties at high density Cross-check with the predictions of BBG theory

High density behavior neutron starsneutron stars

Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC

γ

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

)sin()cos(

43

41)(cos1)( 2220

ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane

ΔΦ=0 rarr Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation Φ0=0 rarr sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ photon angle vs beam axisAverage over reaction planes

All probedRotating angles

36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection

Angular distribution of the extra-yield (prompt dipole) anisotropy

Accurate Angular Distrib Measure Dipole Clock

Martin et al Simulations

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s (D

R)

Central collisions

pn

r

arXiv07073416

DR = (NZ)2 (NZ)1

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)

Conclusions optimistic

Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density

It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables

VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)

Conclusions and Perspectives -II-

γ

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm

N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft

Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay

Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin

Dou

ble

ratio

s

Central collisions

pn

r

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Transverse flow of light clusters 3H vs 3He

mngtmp mnltmp

129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor mngtmp

TritonHelium transverse flow ratiosmaller for mngtmp

Good sensitivity to the mass splitting

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

dppddp )sin(Set of coordinates

)sin( p = 260 MeVc Δp = 10 MeVc

t = 0 fmc t = 100 fmc

)cos(3

23

pV

The variance of the distribution function

p = 190 MeVc Δθ = 30deg

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume p = 190 MeVc θ = 20deg120)(2 Ff E

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124 EA = 50 MeVA b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
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• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles asy-stiffBlack circles asy-soft

Asy-soft small isospin migration

Fe fast neutron emission

Ni fast proton emission

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
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• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)

AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Angular distributions alignment characteristics

plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSnSn

112

124

AZNR

AfZNY

12221

2

2

2ln

)(exp)()(

not very sensitive to Esym 124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffTXLiu et al

PRC 2004

50 AMeV

(central coll)

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
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• Slide 28
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• Slide 31
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• Slide 33
• Slide 34
• Slide 35
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• Slide 37
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• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2

RP = 1 ndash c RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

P IIIII2R

IIIII2R

Imbalance ratios

If

then

50 MeVA 35 MeVA

bull Larger isospin equilibration with MI

(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
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• Slide 21
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• Slide 23
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• Slide 25
• Slide 26
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• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

124Sn + 64Ni 35 AMeV ternary events

NZ vs Alignement Correlation in semi-peripheral collisions

Experiment Transp Simulations (12464)

Chimera data see EDe Filippo PRussotto NN2006 Contr Rio

Asystiff

Asysoft

VBaran Aug06

Asystiff more isospin migration to the neck fragments

Histogram no selection

EDe Filippo et al PRC71(2005)

φ

vtra

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48

Au+Au 250 AMeV b=7 fm

Z=1 dataM3 centrality6ltblt75fm

Difference of np flows

Larger effects at high momenta

Triton vs 3He Flows

pn mm

Mass splitting Transverse Flow Difference

MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48