Constraints on symmetry energy and n/p effective mass splitting with HICs Yingxun Zhang ( 张英逊 ) 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 China Institute of Atomic Energy IWND2012, Dec , Shenzhen, China

Outline 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

Isospin asymmetric Equation of State S( r ) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetric EOS. However, S( r ) uncertainty 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 ) (MeV) 1, Symmetry energy and n/p effective mass splitting

Besides depending on the nuclear density, the symmetry energy also depends on the momentum or energy of a nucleon. S(  )=K+S loc (  )+S nlc ( ,k) For cold nuclear matter

Constraining Symmetry 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+, ……) 1.the symmetry energy information can be extracted. Indirectly! (depends on models) compare with the prediction from the transport model,

Recent progress: constraints on symmetry energy at subsaturation density 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, ……. ……. ImQMD (DR, Ri, R 7 ) 50MeV/A, 35MeV/A, Challenges in the constraints on symmetry energy: Different in detail ！ M.B.Tsang, Yingxun Zhang, et.al., PRL2009 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 ……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, ….. Y.X.Zhang, et.al., PLB664, 145(2008); from BALi, et.al., PRL and PLB Example, 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.

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), DR(t/He3),.. ……. Here, we would like to use the MSU data to constrain the symmetry energy and n/p effective mass splitting simultaneously by comparing with the transport model calculations. 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).

1.The Skyrme parameter sets have been adjusted for fitting the properties of nuclear matter, binding energy, actinide fission barrier, masses, …… Thus, E 0, K 0, S 0, L, K sym, m*_s, m*_v, ……. are correlated. 2.In Skyrme EDF, one can easily choose different values S 0, L, K sym, m*_s, m*_v for similar K_0. 3.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. One of best choices in transport models is to use full Skyrme EDF

New version of ImQMD YX Zhang, Li, Liu, Tsang(2012) Changes: 2, Probing the symmetry energy and n/p effective mass splitting

Para. Rho_0 E0E0 K0K0 Q0Q0 JLK sym m*_s m*_n/m*_p SLy <1 SkI <1 SkM* >1 Gs >1 Small LLarge 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 K 0 = 230 ± 20MeV, S 0 = 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 The Larger the L is, the smaller the symmetry energy at <rho0 is. The larger the U sym is, the larger the n/p ratio is Zhang, Li, Liu, Tsang (2012)

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. R i =(2X-X AA -X BB )/(X AA -X BB ) 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) m*_p) R i is more sensitive to L than n/p effective mass splitting. A=124Sn, B=112Sn

Chi-square analysis on Ri(y) Chi-Square SLy49.41 SkM*1.62 SkI Gs22.52 The Ri(y) data fit the results from SkM* among four parameter sets. SkM*: S 0 =30MeV, L=46Mev, K sym =-156MeV, m*=0.79 and m* n >m* p The calculated results of Ri from SLy4 and SkM* can fall in the data range. For SLy4 and SkM*, they have S 0 =30-32MeV, L=46MeV

n/p and DR(n/p) ratios as a function of kinetic energy E beam =50AMeV, 124 Sn+ 124 Sn, 112 Sn+ 112 Sn DR(n/p)=R n/p (124)/R n/p (112) 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 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. The sensitivity of DR(n/p) to n/p effective mass splitting decrease due to more and more violent NN collisions. Cross over SLy4 (S 0 =32MeV, L=46MeV, m* n <m* p ) SkM*(S 0 =30MeV, L=46MeV, m* n >m* p )

3, Conclusion 1, neutron proton effective mass splitting (isospin dependent MDI) plays an important role on the Y (n)/Y (p) ratios of transverse emitted nucleons at high kinetic energy. 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. (SkM*parameter set, S 0 =32, L=46, Ksym=-156, m*/m=0.69 and mn*>mp*). 4, The n/p effective nucleon masses should be further studied at incident energy below 200 MeV per nucleon and more calculations are needed.

Thanks for your attention!

Charge distribution Weak dependence on the parameters we selected E beam =50AMeV