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HIRFL-RIBLL 合作体第 2 次会议,上海. Constraints on symmetry energy and n/p effective mass splitting with HICs. Yingxun Zhang ( 张英逊 ). China Institute of Atomic Energy. Outline. 1, Symmetry energy and n/p effective mass splitting.

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Constraints on symmetry energy and n/p effective mass splitting with HICs

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Constraints on symmetry energy and n/p effective mass splitting with HICs

Yingxun Zhang (张英逊)

China Institute of Atomic Energy


1, Symmetry energy and n/p effective mass splitting

2, Probing symmetry energy and n/p effective mass splitting with new version of ImQMD

A, new version of ImQMD (ImQMD-Sky)

B, Ri and Ri(y)

C, DR(n/p)

D, DR(n/p) at higher beam energy

3, Conclusions

S(r) (MeV)

1, Symmetry energy and n/p effective mass splitting

Isospin asymmetric Equation of State

It is a fundamental properties of nuclear matter, and is very important for understanding

  • properties of nuclear structure

  • properties of neutron star

  • properties of heavy ion reaction mechanism

S(r) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetric EOS. However, S(r) uncertainty

  • ConstrainingSymmetry energy with heavy ion collisions

  • Heavy Ion Collisions

    • large regions of r, T, d ,

  • measure isospin sensitive observables, such as: the N/Z ratios of the emitted particles (n/p ratios, isospin diffusion, t/He3, N/Z ratios of IMFs, flow, pi-/pi+, ……)

  • compare with the prediction from the transport model,

the symmetry energy information can be extracted. Indirectly! (depends on models)

Recent progress: constraints on symmetry energy at subsaturation density

M.B.Tsang, Yingxun Zhang, et.al., PRL2009

  • Ri: M.B. Tsang, Yingxun Zhang, LWChen, BALi, M.Colonna, Coupland et al

  • DR(n/p): Famiano, BALi, Yingxun Zhang, S.Kumar, YGMa, ZQFeng , ……

  • IAS: Danielewicz, et.al.,

  • PDR(Pb): A. Klimkiewicz, ….

  • N-Star,A.Steiner, ….

  • FRDM: P. Moller, .. ; Mass: M. Liu, FSZhang, et.al. ,

  • M_12, F.Amorini, …….

  • alpha-decay, JM Dong, WZuo, …

ImQMD (DR, Ri, R7) 50MeV/A, 35MeV/A,

Challenges in the constraints on symmetry energy:

Different in detail !

  • different NN interactions or EDF (Skyrme, Gogny, …..) or cross sections are adopted among these models

Momentum dependence of symmetry potential is the most important one among these factors


Y.X.Zhang, et.al., PLB664, 145(2008); from BALi, et.al., PRL and PLB

……momentum dependence of symmetry potential, which would lead to very different magnitude and density …, effective mass of nucleons…, is expected to significantly affect the n/p ratios, …..

However, Momentum dependence of symmetry potential (n/p effective mass splitting)is Uncertainty! We need to constrain it as well as density dependence of symmetry energy.

Besides depending on the nuclear density, the symmetry energy also depends on the momentum or energy of a nucleon.


For cold nuclear matter



  • Constraints on the n/p effective mass splitting (mn*>mp*) has been obtained by analyzing nucleon-nuclei optical potential data. (B.A.Li, C. Xu, et.al., PRC2006,2010).

CXu,BALi,LWChen, PRC82,054607

  • Several works has been done for proposing the HIC observables which are sensitive to the momentum dependence of symmetry potential(or n/p effective mass splitting).

  • J.Rizzo, et.al., Phys.Rev.C (2005), n/p (p_t)

  • H.H.Wolter, et.al.,; t/He3 (p_t) ;

  • Z.Q Feng, et.al. PLB2012, DR(n/p) (pt), DR(t/He3) (pt),

  • …….

Here, we would like to constrain the symmetry energy and n/p effective mass splitting simultaneously by comparing HIC data with the transport model calculations.

One of best choices in transport models is to use full Skyrme EDF

The Skyrme parameter sets have been adjusted for fitting the properties of nuclear matter, binding energy, actinide fission barrier, masses, …… Thus, E0, K0, S0, L, Ksym, m*_s, m*_v, ……. are correlated.

In Skyrme EDF, one can easily choose different values S0, L, Ksym, m*_s, m*_v for similar K_0.

If one use the Skyrme interaction in transport models, one could get the constraints on Skyrme parameters, also on symmetry energy and n/p effective mass splitting from reaction data simultaneously.

2, Probing the symmetry energy and n/p effective mass splitting

New version of ImQMD

YX Zhang, ZXLi, HLiu, Tsang(2012)


Select four parameter sets

K0 = 230 ± 20MeV, S0 = 32 ± 2MeV,

different L and n/p effective mass splitting.

Density dependence of symmetry energy , and the symmetry potential as a function of nucleon energy

Zhang, Li, Liu, Tsang (2012)

  • The Larger the L is, the smaller the symmetry energy at <rho0 is.

  • The larger the Usym is, the larger the n/p ratio is

Isospin diffusion and isospin transport ratios as a function of rapidity

A=124Sn, B=112Sn

Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy and n/p effective mass splitting.

For m*n<m*p, the isospin diffusion process is accelerated due to larger Lane potential at subsaturation density.


In absence of isospin diffusion R=1 or R=-1,

R~0 for isospin equilibrium

Ri(SLy4, L=46MeV, m*_n<m*_p)<Ri(SkM*, L=46MeV, m*_n>m*_p) <Ri(SkI2, L=104MeV, m*_n<m*_p)<Ri(Gs, L=93MeV, m*_n>m*_p)

Riismore sensitive to L than n/p effective mass splitting.

The calculated results of Ri from SLy4 and SkM* can fall in the data range.

For SLy4 and SkM*, they have S0=30-32MeV, L=46MeV

Chi-square analysis on Ri(y)

The Ri(y) data fit the results from SkM* among four parameter sets.


S0=30MeV, L=46Mev, Ksym=-156MeV, m*=0.79 and m*n>m*p

n/p and DR(n/p) ratios as a function of kinetic energy


Ebeam=50AMeV, 124Sn+124Sn, 112Sn+112Sn

  • The Larger the L is, the smaller the n/p ratio is.

  • m*n<m*p enhance the Y(n)/Y(p) ratios at higher kinetic energy region.

  • DR(n/p) ratios are sensitive to the n/p effective mass splitting.

Y(n)/Y(p) and DR(n/p) are more sensitive to n/p effective mass splitting than L

n/p and DR(n/p) at different beam energy

Cross over

SLy4 (S0=32MeV, L=46MeV, m*n<m*p)

SkM*(S0=30MeV, L=46MeV, m*n>m*p)

  • For higher beam energy, the Y(n)/Y(p) obtained with m*n>m*p are greater than that with m*n<m*p cases at lower beam energy.

3, Conclusion

1, Developed a new version of ImQMD which can accommodate the Standard Skyrme interaction in parameters. It can bridge the reaction and structure study by using same EDF.

2, The Ri and Ri(y) support the SLy4 and SkM* interactions, they have L=46MeV.

3, Isospin diffusion data Ri(y) prefer to SkM*, the neutron effective mass is greater than proton effective mass (mn*>mp*), but it is not a strong constraint with deep chi-2 minimum.

4, neutron proton effective mass splitting (isospin dependent MDI) plays an important role on the Y (n)/Y (p) ratios of transverseemitted nucleons at high kinetic energy.

5, The n/p effective nucleon masses should be further studied at intermediate energy per nucleon and more calculations are needed.

合作者: Zhuxia Li (李祝霞)China Institute of Atomic Energy,

Hang Liu (刘航) Texas Advanced Computer center, University of Texas,

M.B.Tsang(曾敏儿)NSCL/Michigan State University

Thanks for your attention!

Charge distribution

Weak dependence on the parameters we selected


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