Probing the density dependence of symmetry energy at subsaturation density with

HICs

Yingxun Zhang (张英逊 )

•China Institute of Atomic Energy•JINA/NSCL, Michigan State Uni.

B.Tsang, Zhuxia Li, P.Danielewicz, W.G.Lynch

outline

① Introduction on Esym() and ImQMD05

② Reaction mechanism Sn+Sn @ 50AMeV

③ the n/p ratio, isospin diffusion, N/Z ratio of IMFs

④ Conclusion and outlook

① Introduction

Esym() is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetry EOS.

)(0,, 42 OEEE sym

It is a fundamental properties of nuclear matter, and is very important for understanding • masses, • fission barriers, • thickness of the neutron skins of neutron-rich nuclei.• properties of NS, ….

Isospin asymmetry nuclear Equation of State

By comparing the HICs Observables with transport model predictions:

So, lot of observables have been proposed•At subsaturation density: n/p ratios, isospin transport ratios, isoscaling, t/3He,C(q) ……•At supersaturation density: pi-/pi+, n/p ratio and flow, C(q), K, ……

How to constrain the Esym() in Lab?

(BALi, Tsang, LWChen, M.Colonna, Q.F.Li, Y.Zhang, ……)

Transport model: ImQMD05 Study the influence of cluster emission mechanism on observables for the intermediate energy HICs

In this research, we focus ourselves on constraining the density dependence of symmetry energy at subsaturation densities by comparing the transport model predictions with the NSCL’s Sn+Sn @ 50AMeV data.

Brief introduction on ImQMD05 the mean fields acting on nucleon wavepackets are derived from Skyrme potential energy density functional

potential energy density functional:

Parameters in Vloc are obtained from standard Skyrme interactions

parameters

3/5

0

3/82

0

2

0

,2

00

1

0

2

)(2

)]([212

gCgg

u spn

isosursur

• Change the symmetry potential in the transport model by varying the

Phase space constraint for considering Pauli principle

Isospin dependent nucleon-nucleon cross sections are adopted, the medium corrections are

The occupation number in cubic of h3 should be small than 1(Pauli principle)

1if

freenp

mednp )/1( 0

freeppnn

medppnn ,0, )/1(

freeppnnnp )(, Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996)

isospin independent Momentum dependence interaction 224

2,,

123

13

60

1051ln57.116

1

2

12

21

1ppfpfpdpdu N

pnNNNmd

Aichelin, et al., PRL58,1926(1987)

and the MDI contributions at T=0MeV are subtracted in order to use the Skyrme interaction parameters and the MDI.

Zhang, Li, PRC71(2005)24606

flow

stopping

Data: Residorf, PRL 92(2004)232301

Several aspects (Such as, collective flow, stopping, charge distributions) have been successfully described by this model

• The reasonable charge distribution is important for prediction the HICs observables.

Zhang, Li, PRC71(2005)24606

Charge distribution

② Reaction mechanism for Sn+Sn at E/A=50MeV

b=2fm

b=6fm

The charge distributions for 112Sn+112Sn at E/A=50MeV for b=2, 6, 8fm. The solid symbols are for stiff symmetry energy case (gamma=2.0) and open symbols are for the soft symmetry energy case (gamma=0.5).

The contour plots for fragment charge Z vs rapidity at different impact parameters b=2, 6, 8 fm for 112Sn+112Sn with soft symmetry energy cases (gamma=0.5).

Charge distribution depend on the stiffness of EoS

Reaction mechanism of fragments productions depend on the impact parameters

③ the n/p ratio, isospin diffusion, N/Z ratio of IMFs

A. n/p ratio and DR(n/p) ratio

• more pre-equilibrium neutrons get emitted from the neutron rich 124Sn+124Sn system

• relatively more pre-equilibrium neutrons are also emitted in the calculations with softer symmetry energy

b=2fmkp

knpn dEdM

dEdMR

/

//

• the emitted nucleons directly feel the symmetry potential• n/p ratio is related to the stiffness of symmetry potential at subsaturation density (BALi, PRL(1997))

•Significant cluster and sequential decay effects are at low energy!

• Over the whole energy range for both free and coalescence-invariant DR(n/p) the data seem closer to the gi=0.5 calculation

• For very small gi, the system completely disintegrated, DR decreases and approaches the limit of reaction system. the double ratio values peak around i~0.7.

• By comparing with data, the i=[0.4,1.05] within <2

DR(n/p)=Rn/p(124)/Rn/p(112)Data from Famiano, PRL97, 052701(2006)

Detailed comparison with data by varying i

Tsang, et.al., PRL102(2009) i

symE 03/2

0 /5.17/5.12

B. isospin diffusion

Ri=(2X-XAA-XBB)/(XAA-XBB)

• X is the isospin dependent observable. A, B refer to 124Sn, 112Sn

• Time scale of the isospin diffusion ~100fm/cIsospin diffusion

b=6fm

(isospin transport ratio or isospin imbalance ratio)

•Theory: X is the , the isospin asymmetry of emitting source• Exp: X is the isoscaling parameter , ln(Y(7Li)/(Y(7Be)))• There is linear relationship between Xth and Xexp, So, R(Xth)=R(Xexp)

124112

• Detailed comparison with data

Tsang,, et.al., PRL102,122701(2009)

Consistent 2 analysis of these observables within ImQMD model provides

i

symE 03/2

0 /5.17/5.12

with gamma_i=[0.4,1.0]

• Ri depend on the X definition. The differences reflect the isospin diffusion mechanism for peripheral collisions. Isospin diffusion mainly occurs around neck region.

Observable from heavy fragments

C. N/Z ratio of IMFsN/Z ratios from bound fragments (Z=3-8)

complementary to n/p ratios• N/Z ratio of IMFs depend on the density dependence of symmetry energy• After decay, Data from NSCL favor the soft symmetry energy

• at low energy, the N/Z ratio of IMFs obtained with stiff symmetry energy case is larger than that with soft symmetry energy case.•Coulomb effects are important at lower kinetic region

④ Conclusions and outlook:• n/p ratio and DR(n/p) ratio of the emitted nucleons s

trongly depend on the density dependence of symmetry energy, and the significant cluster emission effects are at low energy on the DR ratio.

• Isospin transport ratio depend on the density dependence of symmetry energy and its values also depend on the tracer. The difference reflects the isospin diffusion mainly occurs around the neck region.

• Detailed comparison with data of DR(n/p), Ri, and R7 have been done, and the analysis provide consistent constraints on the density dependence of symmetry energy from ImQMD model.

• N/Z ratio of the IMFs also depend on the density dependence of symmetry energy, and the sequential decay effects are important.

“ Constrain the Esym() is a complex problem, and further work on the theory and experiment are needed”

• There is no transport models do the MF and NN cs consistently.

• Uncertainty of the transport model need to be reduced

• More and accurate data are needed for developing the transport model in future.

Thanks for your attention !