The National Superconducting

Cyclotron Laboratory@Michigan State University

Bet ty Tsang

Exploring the Equation of state of neutron-rich matter with Heavy Ion Reactions

International Workshop on Nuclear Dynamics on heavy ion

reactions and neutron stars, July 10-14, 2007, Beijing, China

Outline:

NSCL/MSU

Reaction programs @ NSCL

Rare Isotope Productions

Transfer Reactions

Equation of state of neutron-rich matter – current

experimental status

Refining reaction theories

Fragment systematics

Transport Equation simulations

Summaries and Outlooks

Michigan

The National Superconducting Cyclotron Laboratory @ Michigan State University

A national user facility for rare isotope research and education in nuclear science, astro-nuclear physics, accelerator physics, and societal applications

~ 300 employees, incl. 50 undergraduate and 50 graduate students, 25 faculty

User group of over 600 CCF users

The National Superconducting

Cyclotron Laboratory@Michigan State University

Nuclear Physics @ the K500K1200 Facility (CCF)

Nuclear Reactions:

•Rare Isotope Productions

•Transfer Reactions

•Equation of state of neutron-

rich matter

•Refining reaction theories

Nuclear Structure:

•Accessibility of driplines

•Physics of weakly bound nuclei

•Isospin dependence of nuclear

properties

•Evolution of shell structures

•etc

Accelerator Physics

•RIA related research

Nuclear Astrophysics

•Synthesis of elements

•Evolution of supernovae

•Neutron star physics

National Superconducting Cyclotron Laboratory

K500

World’s first superconducting cyclotron (1982)

K1200World’s most powerful superconducting cyclotron (1989)

A1900

Coupled Cyclotron Facility (2000)

Rare Isotope Production Mechanism• Primary beams: 40,48Ca,

58,64Ni at 140 MeV per nucleon; unstable 68Ni, 69Cu and 70Zn beams at 90 MeV per nucleon and 86Kr at 64 MeV per nucleon

• ~2000 cross-sections

• EPAX over-predicts isotopes at the p/n extremes

• Study of production model suggests that sequential decays wash out the details of the prefragment stage of the reactions

40Ca+Be

48Ca+Be

Relation between cross-sections and average

binding energy (BE/A)

Mass measurements

of rare isotopes

Sensitivity ~TOF

Extrapolation of

cross-sections to n-

rich and dripline

isotopes

Can be described

with the use of

statistical or phase

space model

Neutron Number N

Pro

ton

Nu

mb

er Z

3/2AaAaB SV 3/1)1(

A

ZZaC

A

ZAasym

2)2(

Symmetry Energy in Nuclei

Inclusion of surface

terms in symmetry

2

23/2 )2()(

A

ZAAaAa SV

symsym

Hub

ble

ST

Crab Pulsar

Size & Structure of Neutron Star depends on EOS

D. Page

EOS influenceR,M relationship

maximum mass.

cooling rate.

core structure

Birth of a Neutron Star

July 4, 1054, China

July 5, 1054, N. America

Cra

b P

uls

ar

R. Lacey

E/A (, ) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A

Danielewicz, Lacey, Lynch, Science 298,1592 (2002)Results from Au+Au flow

(E/A~1-8 GeV) measurements

include constraints in

momentum dependence of the

mean field and NN cross-

sections

Heavy ion collisions :

Isospin Dependence of the Nuclear Equation of State

• The density dependence of

symmetry energy is largely

unconstrained.

• Pressure, i.e. EOS is rather

uncertain even at 0.

E/A (,) = E/A (,0) + 2S()

= (n- p)/ (n+ p) = (N-Z)/A

a/s

2 A/EP

-20

-10

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6

EOS for Asymmetric Matter

Soft (=0, K=200 MeV)asy-soft, =1/3 (Colonna)asy-stiff, =1/3 (PAL)

E/A

(M

eV)

(fm-3

)

=(n-

p)/(

n+

p)

PAL: Prakash et al., PRL 61, (1988) 2518.

Colonna et al., Phys. Rev. C57, (1998) 1410.

Brown, Phys. Rev. Lett. 85, 5296 (2001)

Neutron matter EOS

E/A (, ) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A

• Surface symmetry energy in mass formulae:

– Difficult to disentangle from Coulomb and bulk symmetry energy.

• Energies of GDR and pigmy dipole resonances:

– Extraction is model dependent.

• Difference between neutron and proton rms radii in nuclei:

– Sensitive to dS/d=0– Accuracy of present results are disputed.

– PREX experiment at JLAB.

• (limited precision: rms,n0.06 fm)

• Asymmetry dependence of isoscaler GMR:

– Sensitive to d2S/d2=0

• All above observables are sensitive to ~0• Isoscaling in Heavy Ion collisions: Y1(N,Z)/Y2(N,Z)exp(N+Z)

– 4(Csym/T)D(Z/A)2

– Sensitive to sequential decays

Nuclei and the density dependence of the symmetry energyConstraints and possible measurements

NP

0

0.02

0.04

0.06

0.08

0.1

-2 0 2 4 6 8 10 12

n (fm

-3)

p (fm

-3)

n (

fm-3

)

R (fm)

208Pb

Probes of the symmetry energy with HIC

• Low densities (

80-380

420-620

n/p Experiment 124Sn+124Sn; 112Sn+112Sn; E/A=50 MeV

Scattering Chamber

Famiano et al

N-detection – neutron wall

p-detection: Scattering Chamber

3 particle telescopes

(p, d, t, 3He, …)

WU MicroBall

(b determination)

~6in

n/p Double Ratios (central collisions)

•Role of isoscaler emission:

–Effect of cluster production

clear and theoretically

reproduced by QMD.?

124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double

Rat

io

Double Ratiominimize systematic errors

Center of mass EnergyImQMD: Y.X. Zhang

IBUU04: B.A. Li

xAB, yAB experimental or

theoretical observable for AB

yAB= a xAB+b

Ri(xAB )= Ri(yAB )

Rami et al., PRL, 84, 1120 (2000)

BBAA

BBAAABi

xx

xxxR

2/)(2

Isospin Diffusion--Isospin Transport Ratio

No isospin diffusion between

symmetric systems124

124112

112

Isospin diffusion occurs only

in asymmetric systems A+B124

112

Non-isospin diffusion effects

same for A in A+B & A+A ;same for B in B+A & B+B

Non-isospin transport effects are “cancelled”??

Ri = 1

Ri = -1

Isotope Distribution Experiment

MSU, IUCF, WU collaboration

Sn+Sn collisions involving 124Sn, 112Sn at E/A=50 MeV

Miniball + Miniwall

4 multiplicity arrayZ identification, A

Emission patterns of 7Li & 7Be from 124Sn+112Sn; E/A=50 MeV

V//

CM

0

Y(7Li) enhanced from 124Sn Y(7Be) enhanced from 112Sn

Isospin transport observable

Ratio Y(7Li)/Y(7Be)

Mainly dominated by Coulomb

112Sn+124Sn

V//(au)

Y(7Li) enhanced from 124Sn

Y(7Be) enhanced from 112Sn

How to observe isospin transport ?

BBAA

BBAAABi

xx

xxxR

2

112Sn+124Sn

Coulomb & other

(preequilibrium &

sequential) effects

are “cancelled”

BBAA

BBAAABi

xx

xxxR

2

Rami et al., PRL, 84, 1120 (2000)

Isospin Transport Ratio

Transport Equation Simulations

• Diffusion occurs within

120 fm/c.

• More mixing with soft S()

– consistent with large

Esym at

Transport Equation Simulations

• Explicit secondary decay correction gives same result.

• Stiff S() favored.

• Momentum-isospin dependence?

Tsang et al. PRL 92, 062701(2004)

esymint

(/0

g=2

SKM

Constraints from Isospin Diffusion Data

M.B. Tsang et. al.,PRL 92, 062701 (2004)

L.W. Chen, C.M. Ko, and B.A. Li,PRL 94, 032701 (2005)

C.J. Horowitz and J. Piekarewicz,PRL 86, 5647 (2001)

B.A. Li and A.W. Steiner,nucl-th/0511064

Summary & Outlook I: Improve

measurements on n/p double ratios

and transport model calculations

Investigate model

dependencies of the

isospin dependent in-

medium cross sections

and effective masses

that must be better

constrained.

ImQMD : Y.X. Zhang,

Z.H. Li

BUU: Y.X. Zhang, P.

Danielewicz

Summary and Outlook II : Tightening the constraints at

sub-saturation density

• Improving and understanding better the impact parameter determination.

• Changing the incident energy

• Improving the constraints on S(0), m*?

• Improving the constraints on the isospin dependent in-medium cross sections.

• Investigating with other observables

ImQMD : Y.X. Zhang, Z.H. Li

BUU: Y.X. Zhang, P. Danielewicz

Experiment Correlation functions with HiRA

• Calculations predict the height and

width of proton-proton correlations

are sensitive to the density

dependence of the asymmetry term.

– width provides more accurate

information than height.

Chen

et al., PR

L 9

0 1

62701 (2

003).

Verd

e (2004)

The High Resolution Array (HiRA)

32 strips v. (front)Beam

Si-DE 65 m

32 strips v (front)

Si-E 1.5 mm

pixel

32 strips h. (back)

A State-Of-The-Art Silicon Detector Array for studying transfer reactions, resonance spectroscopy, interferometry, …

Extrapolation of neutron-rich isotope cross-sections from 140

MeV per nucleon 48Ca and 64Ni beam

M. Mocko, Z.Y. Sun, L. Andronenko, M. Andronenko, F. Delaunay,

M. Famiano, W. A. Friedman, V. Henzl, D. Henzlova, H. Hui, X.

D. Liu, S. Lukyanov, W. G. Lynch, A. M. Rogers, M. B. Tsang, and

M. S. Wallace

64 MeV per nucleon 86Kr beam

N. Imai,4 H. Iwasaki,5 T. Motobayashi,4 M. Niikura,6 T. Onishi,5

H. Sakurai,5 H. Suzuki,5 E. Takeshita,7 S. Takeuchi,4

Isospin fractionation in nuclear multifragmentation

H.S. Xu, M.B. Tsang, T.X. Liu, X.D. Liu, W.G. Lynch,

W.P.Tan and G. Verde, L. Beaulieu, B. Davin, Y.

Larochelle, T. Lefort, R.T. de Souza, R. Yanez, V.E.

Viola, R.J. Charity, and L.G. Sobotka, Phys. Rev. Lett.

85, 716 (2000).

Isospin diffusion observables in heavy ion reactions

T.X. Liu, W.G. Lynch, X.D. Liu, R. Shomin, W.P. Tan, M.B. Tsang, G.

Verde, A. Wagner, H.F. Xi, H.S. Xu,

B. Davin, Y. Larochelle, R. T. de Souza, (Indiana University)

R.J. Charity, and L.G. Sobotka, (Washington University)

The High Resolution Array (HiRA) for rare isotope beam experiments

M.S. Wallace, M.A. Famiano, M.-J. van Goethem, F. Delauney, A. Rogers,

W.G. Lynch, J. Clifford, J. Lee, S. Labostov, M. Mocko, L. Morris, B.E. Nett,

D.J. Oostdyk, R. Krishnasamy and M.B. Tsang,

R.D. de Souza, S. Hudan IUCF,

R.J. Charity, J. Elson and L.G. Sobotka, Washington University,

A. Moroni, INFN Milano, Italy