重离子碰约束对称能中的相关问题

张英逊 (Yingxun Zhang)

中国原子能科学研究院（ CIAE ）

2015 强子物理与核物理前沿研讨会Frontiers in Hadron and Nuclear Physics (FHNP’15)

国科大， 1 月 10 日，怀柔

Outline1, Nuclear equation of state and symmetry energy

2, Progress and Challenges on the constraints of symmetry energy

3, Influence of L, fI on HIC observables • isospin diffusion • single Y(n)/Y(p) and Double Y(n)/Y(p) ratios

spectra for free nucleons• Coalescence invariant Y(n)/Y(p) and DR(n/p)• comparison to the data

4, Summary and outlook

S(r)

(MeV

)

Symmetry energy and EOS

)(0,, 42 OSEE

pair22

s3/4

C3/1

sv )ZN/()ZN(aA)1Z(ZaAaaA/)Z,A(E

Nuclei

Isospin asymmetric nuclear matter, EOS

S0: symemtry energy coefficientL: slope of density dependent of symmetry energyKsym: curvature of density dependent of symmetry energy

Symmetry energy

Density dependent of symmetry energy

Esy

m (r

B)

(MeV

)

rB/r01 2 30

Asy-stiff

Asy-soft

Importance of the Nuclear Symmetry Energy in Nuclear and Astrophysics

supernovae

Heavy ion collisions in the Fermi energy regime;multifragmentation

supernova simulationscovers large range of thd. conditions

Nuclear structure(neutron skin thickness, Pygmy DR, IAS)

Slope of Symm Energy

Light cluster correlations at very low density

From Hermann’s talk

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

Strategies for constraining the symmetry energy

• Astrophysical measurements• Nuclear structure• Heavy Ion Collisions

large regions of r, T, d ,

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

predictions from the transport model, in which the different symmetry potential can be used.QMD, BUU,AMD, SMF, ……

HIC observables: n/p ratios and isospin diffusion, ……

Y(n)/Y(p); t/3He, p+/p-

Projectile

Target

124Sn

112Sn

Isospin Diffusion; low r, Ebeam

Tsang et al., PRL 92 (2004) 062701BALi, et al., PRL78(1997)1644

Yingxun Zhang et al., PLB664(2008)145 LWChen, et al., PRL72(2005)064309

Famiano, et al., PRL97,0522701(2006)

Constraints on the density dependence of symmetry at subsaturation density

M.B.Tsang, Y.X.Zhang, et al., PRL102,122701(2009) (222 cites)

i

symE 03/2

0 /5.17/5.12

Detailed comparison with data by varying gi

Consistent c2 analysis of these observables within ImQMD model provides

with gamma_i=[0.45,0.95]

M.B.Tsang, Yingxun Zhang, et.al., PRL2009 Lattimer, EPJA 50 (2014) 40

Consensus on symmetry energy have been obtained at subsaturation density,

Challenges on constraining the symmetry energy

Symmetry energy at r<0.05ro, T<10 MeV is dominated by correlations and cluster formation

J.B. Natowitz et al, PRL 104 (2010) 202501

Esym

(n)/

Esym

(n0)

MDI, NN-ND, threshod, ……

1. How to understand the difference on the constraints on the symmetry energy?

2. Constraints at very low density3. Constraints at supra-normal density with HICs

• 不同模型采用相同的有效核力不同

• Vsym( ,r k)=Vloc(r)+Vnlc(r,k)

• ……

差别的来源

更多观测量来约束理论上的不确定性

• 理论提供更多同位旋敏感观测量

• 新的实验测量

New version of ImQMD

Y.X. Zhang, M.B.Tsang, Z.X. Li, HLiu, PLB(2014)

Changes:

输运模型中采用与结构研究中相同的有效核力

two-body term three-body termMom. dependent

density dependent of symmetry energy from Skyrme interaction in HF:

Density dependent

考虑动量相关势对重离子碰撞观测量的影响

L.Ou, Z.X.Li, Y.X.Zhang, M.Liu, PLB697(2011)

Zhang, et al., PRC85,024602(2012)

Momentum dependent symmetry potential － >effective mass splitting

Effective mass splitting

R. Chen et al., PRC 85, 024305 (2012).

K-mass E-mass

M_n*>m_p* M_n*=m_p* M_n*<m_p* ?????

Para. Rho_0 E0 K0 Q0 J L Ksym m*_s m*_n/m*_p

SLy4 0.16 -15.97 229.91 363.11 32 46 -120 0.69 <1

SkI2 0.158 -15.78 240.93 339.70 33 104 71 0.68 <1SkM* 0.16 -15.77 216.61 386.09 30 46 -156 0.79 >1

Gs 0.158 -15.59 237.29 348.79 31 93 14 0.78 >1

Small L Large L

m_n*<m_p* SLy4 (L=46MeV) SkI2 (L=104MeV)

m_n*>m_p* SkM* (L=46MeV) Gs (L=93MeV)

Select four parameter sets

K0 = 230 ± 20MeV, S0 = 32 ± 2MeV, m*_s=0.7+/-0.1 different L and n/p effective mass splitting.

Influence of Skyrme force to HIC observables

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

• 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

Zhang, Tsang, Li, Liu,, PLB732,186(2014)

• Isospin diffusion and isospin transport ratios as a function of rapidity

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

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

In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium

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

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)

Ri is more sensitive to L than n/p effective mass splitting.

A=124Sn, B=112SnZhang, Tsang, Li, Liu,, PLB732,186(2014)

50AMeV, b=2fm

Isospin diffusion R(n/p) and DR(n/p)

D.D.S.Coupland, et al., arXiv:1406.4546

Zhang, Tsang, Li, Liu,, PLB732,186(2014)

Mn*>mp*???

• 新观测量的探索，出射轻粒子角分布各向异性Ar+Au 轻粒子动力学发射

Qianghua Wu, Yingxun Zhang, Z.G.Xiao, et.al. PRC(2015) in press

Colin, PRC

4, Summary and outlook1, 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, it is close to the results from neutron skin analysis.

3, Questions?For neutron-rich dense matter, 1) effective mass splitting ?2) isospin-independent momentum dependent interaction in

the transport model? …

Thanks for your attention!

Collaborators: 李祝霞 , M.B.Tsang, P.Danielewicz, W.G.Lynch, D.D.S.Coupland, R.Hodges, H.Liu, Qianghua Wu, Zhigang Xiao, Rensheng Wang, Yan Zhang, 王宁