• Motivation

• Current status

• Outlook

This work was supported in part by:The Robert A. Welch Foundation: Grant Number A-1266 and,

The Department of Energy: Grant Number DE-FG03-93ER40773

D.V. Shetty, G. A. Souliotis, D. Rowland, A. Keksis, E. Bell, M. Jandel, M. Veselsky, R. Laforest, E. Ramakrishnan, H. Johnston,

L. Trache, F. Gimeno-Nogues, A. Ruangma

Cyclotron Institute, Texas A&M University,College Station, Texas 77843

S.J. Yennello

Using Isoscaling to understand the symmetry energy of the nuclear equation of

state.

A heavy nucleus (like 208Pb) is 18 orders of magnitude smaller and 55 orders of magnitude lighter than a neutron star !

Atomic nuclei & Neutron star

( two vastly different systems )

Yet bounded by a common entity, the nuclear Equation Of State (EOS) !

H. Huber et al, Phys. Rev. C 50 (1994) 1287(R)

Softer EOS leads to a smaller star mass and

radius for a given central density

EOS in Astrophysics and Stellar Properties Size & Structure of Neutron Star depends on

EOS

EOS influence R,M relationshipmaximum mass.cooling rate.core structure

Host of nuclear EOS employed in astrophysical modeling of neutron star & supernova explosion

Still leaves a wide range of possibilities !

Some are excluded by causality & some by known masses of existing neutron

stars F. Weber, IoP publishing, Bristol (1999)

Esym(

= (n - p)/(n + p)

Not well constrained

Danielewicz, Lacy, Lynch, Science 298,1592 (2002)

Pre

ssur

e (M

eV/f

m3 )

What is known about the EOS of symmetric matter?

Multifragmentation reaction (Probing the low density dependence)

Observables sensitive to the asymmetry term in the EOS ?

Moderate density ( < 1.5 o) :Fragment isotope distribution, isotopic & isobaric yield ratios Isospin distillation/fractionation, relative n & p densitiesIsospin diffusionNuclear stopping & N/Z equilibrationPre-equilibrium emissionParticle - particle correlationLight cluster production

High density ( > 1.5 o) : Collective flowSubthreshold particle production

An inhomogeneous distribution of the neutrons and An inhomogeneous distribution of the neutrons and protons within the system is predicted, resulting in a dilute protons within the system is predicted, resulting in a dilute

neutron rich (N/Z > 1) gas (light clusters) and a dense neutron rich (N/Z > 1) gas (light clusters) and a dense and symmetric (N/Z ~ 1) liquid (heavy fragments) and symmetric (N/Z ~ 1) liquid (heavy fragments)

Isospin distillation in asymmetric (N/Z > 1) nuclear matter

( H. Muller & B. Serot. Phys. Rev. C 52, 2072 (1995) )

Studying isospin distillation

Measure the yields of the light clusters (gas phase)

Determine the n & p densities

Compare them from one reactions to another with different isospin (N/Z)

Relative n density

Relative p density

Relative n & p density from isotope & isotone yields

free neutron & proton densities

N

n

n

ZNYZNY

ZkNYZkNY

1,

2,

12

12

),(/),(

),(/),(

Z

p

p

ZNYZNY

kZNYkZNY

1,

2,

12

12

),(/),(

),(/),(

Z

p

p

N

n

nCZNY

ZNYR

1,

2,

1,

2,

1

221 ),(

),(

TZNBZNZN

Zp

Nn eTFTPZNY /),(

,, )()(),(

Relative n & p densities :

58Ni + 58Ni (reaction 1, N/Z = 1.07))

58Ni + 58Fe (reaction 2, N/Z = 1.15 )

58Fe + 58Fe (reaction 2, N/Z = 1.23)

58Ni + 58Ni (reaction 1, N/Z = 1.07)

Relative n & p density

&

&@ 30, 40, 47

MeV/nucl.

1,

2,

,1,

2,

p

p

n

n

If the clusters in reaction 2 are more neutron-rich than in reaction 1

Relative n density ,

Relative p density ,

> 1

< 1

1,

2,

n

n

1,

2,

p

p

Ratio of isotopic yields58Ni, 58Fe + 58Ni, 58Fe 30 MeV/nuc

R21(N,Z) = C eN + Z

NiNinn

/

NiNipp

/

Relative neutron and proton densities at 30 MeV/nuc

Isotope ratios

Isotone ratios

neutron and proton densities at 30, 40, 47 MeV/nuc

NiNinn

/

NiNipp

/

Isotope ratios

Isotone ratios

ExperimentalSMM model comparison

Excitation energy (MeV/A)

Isotone ratios

Isotope ratios

30 MeV 40 MeV 47 MeV

0.372 0.269 0.23

-0.395 -0.372 -0.32

0.15

0.2

0.25

0.3

0.35

0.4

25 30 35 40 45 50

Beam Energy ( MeV/nuc)

alp

ha

58Fe + 58Fe / 58Ni + 58Ni

Tsang PRC64, 054615 (2002)

Temperature dependence of the scaling parameter

Symmetry energy and the fragment yield distribution in Multifragmentation reaction

Symmetry energy of the primary fragments are significantly lower D. V. Shetty et al, (2004)

Primary fragments

Secondary fragments

EOS and dynamical simulation of fragment production (AMD model calculations)

A. Ono et al, Phys. Rev. C 68 (2003) 051601(R)

D. V. Shetty et al, Phys. Rev. C 70 (2004)

011601(R)

Symmetry energy and the scaling parameter

Csym ~ 18 – 20 MeV ; ~ 0.08 fm-3

Formation of hot neutron rich nuclei in supernova explosion

During supernova II type explosion the thermodynamical conditions of stellar matter between the protoneutron star & the shock front correspond to nuclear liquid-gas coexistence region. Neutron rich hot nuclei can be produced in this region which can influence the dynamics of the explosion contribute to the synthesis of heavy elements

A slight decrease in the symmetry energy co-efficient can shift the mass distribution to higher masses

A. Botvina et al, Phys. Lett. B 584 (2004) 233

Deep InelasticTransfer mechanism can produce neutron-rich heavy residues

Neutron richness

A

FAUST

FAUST has solid angle coverage of 90% from 2.31º to 33.63º, 71% from 1.6º to 2.3º, and 25% from 33.6º to 44.9º.

0.833mg/cm2

2.535mg/cm2

4.778 mg/cm2Mylar

F. Gimeno-Nogues, et al. NIM A 399 (1997) 94http://cyclotron.tamu.edu/sjygroup/external/Detectors/FAUSTWeb/faust.html

Neutron richness

Production of quasi projectiles over a wide range in N/Z from 33Mev/nuc 20Na, 20Ne, 20F + Au

reactions

Rowland, Phys. Rev. C 67, 064602 (2003).

Beam <N/Z>

proj

<N/Z>

DIT

<N/Z>

DIT+evap

<N/Z>

exp

20Na .818 .926 .876 .912

20Ne 1 1.06 .953 1

20F 1.22 1.23 1.02 1.07

Botvina IsoscalingR21 = C exp(’A + ’(N-Z)

30 MeV/nuc 50 MeV/nuc

’ = 0.237±0.038 ’ = 0.186±0.017

’ = (n + p)/2T

’ = (n - p)/2T

28Si + 112,124Sn

Botvina IsoscalingR21 = C exp(’A + ’(N-Z)

28Si + 112,124Sn ; 50 MeV/nuc

E*

(MeV)

’

3 0.31

4 0.20

5 0.19

6 0.18

7 0.17

Al quasiprojectiles

’T’ = (n - p)/2T

MARS Recoil Separator and Setup

PPAC2 Stop T Silicon Telescope:ΔE1, X,Y (Strips)ΔE2, Eresidual

PPAC1 Start T X,Y

Production Target

D1D2

D3

WienFilter

Q1Q2Q3

Q4Q5

Dispersive Image

FinalAchromatic Image

Rotatable ArmReaction Angle: 0-12o (selectable)

MARS Acceptances:Anglular: 9 msrMomentum: 4 %

Beam angle set to: 0o (1.0-3.0o) for Kr+Ni (gr = 3.5o)

4o (2.5-5.5o) for Kr+Sn (gr = 6.5o)

The Superconducting Solenoid Rare Isotope Line at TAMU:

Schematic diagram of the setup for heavy-residue studies from DIC:

Ge

Data usingtargets:

124Sn 112Sn 64Ni

------ EPAX2

Target N/Z Valley of stability 124Sn 1.48 n-rich 118Sn 112Sn 1.24 n-poor 64Ni 1.29 n-rich 60Ni

DIT mechanism can produce neutron-rich heavy residues

Souliotis, Phys. Rev. Lett. 91, 022701 (2003)

Mass Distribution of Germanium from 86Kr(25MeV/u) + 124Sn,112Sn, 64Ni

Comparison: Data/EPAX : 86Kr (25 MeV/u) + 64Ni, 124Sn

For near-projectilefragments and above the projectile N/Z,the cross sectionsare larger.

DIC between massive n-rich nuclei appear to beadvantageousfor very high N/Z RIB production

Scaling of Yield Ratios :

•86Kr+124Sn,112Sn (data inside gr=6.2ο)

R21 (N,Z) = Y2/Y1

R21 = C exp ( α N )

•86Kr+64Ni,58Ni (data outside gr=3.5o)

Isoscaling Parameter α : *

• 86Kr+64Ni,58Ni

R21 = C exp ( α N )

• 86Kr+124Sn,112Sn

α =0.43

α =0.27

* G.A. Souliotis et al., Phys. Rev. C 68, 024605

α = 4 Csym/T ( (Z/A)12

– (Z/A)22

)

Quasi-projectiles 1: n-poor 2:nrich

Isoscaling data from residues of 64Ni (25MeV/nucleon)

R21 (N,Z) = Y2/Y1

R21 = C exp ( α N )

BigSol data

86Kr, 64Ni, 136Xe data: Isocaling parameter vs Δ(Z/A)2:

Quasi-projectiles : E/A ~20-25 MeV

N/Z equilibrated, no effect of pre-eq.

86Kr+124,112Sn* 2.0 MeV/u86Kr+64,58Ni* 2.4 MeV/u

64Ni+124,112Sn64Ni+64,58Ni64Ni+232Th,208Pb* 2.9 MeV/u

α = 4Csym/T ( (Z/A)12

– (Z/A)22

)

c

136Xe+124,112Sn136Xe+64,58Ni136Xe+232Th,Au* 2.5 MeV/u

Data : 86Kr+124,112Sn 86Kr+64,58Ni 64Ni+ Ni,Sn,Th-Pb 136Xe+Ni,Sn,Th-Au

Calculation:Fermi Gas (K=13)Mononucleus expansionmodel (L. Sobotka, J. Toke)

Csym = c T / 4

Variation w.r.t excitation energy:

Projectile residue distributions from peripheral to mid-peripheral collisions show enhanced production of neutron –rich nuclei Heavy-Residue Isoscaling can be used as probe of N/Z Equilibration, Esym()Multifragmentation reactions may be able to distinguish between various functional form of the density dependence of the symmetry energySymmetry energy can be significantly below saturation density and could be interesting in the studies relating to the elemental abundances in core collapse supernova explosion

Effect of Secondary Decay on isoscaling parameters needs to be understood Comparisons with Reaction Models:

Extension of studies using higher N/Z beams and heavy targets

Summary and Outlook