利用重离子碰撞确定对称能 密度依赖形式 核物理前沿热点问题研讨会 10月27日 广西 桂林 张英逊 中国原子能科学研究院 合作者： 李柷霞 (CIAE) P.Danielewicz, M.B.Tsang, W.G.Lynch (NSCL/MSU)

Outline 1.Symmetry energy 2.Constraining the symmetry energy with HICs  ImQMD05  the influence of symmetry potential In-medium NN cross section Impact parameter Cluster formation on heavy collision observables for Sn+Sn at 50AMeV 3.Conclusions and discussion

What is the Symmetry Energy? Neutron Number N Proton Number Z Symmetry Energy in Nuclei Inclusion of surface terms in symmetry Hubble ST Crab Pulsar Liu’s talk

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 masses, fission barriers, thickness of the neutron skins of neutron-rich nuclei. properties of Neutron Star, …. Isospin asymmetric nuclear Equation of State S( r ) (MeV) Symmetry energy

measure 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, in which the different symmetry potential can be used. Strategies for constraining the symmetry energy 1, Astrophysical measurements 2, Nuclear structuer 3, Heavy Ion Collisions large regions of r, T, d, the symmetry energy information can be extracted. Indirectly! (depends on models)

2, Constraining the symmetry energy with HICs a), Probes is sensitive to the density dependence of symmetry energy (from theory) b), Experiment (Intermediate energy Heavy Ion Collisions) (n/p, isospin diffusion, pi-/pi+, n,p flow, t/He3,…) BALi, ZXLi, LWChen, QFLi, YXZhang, GCYong, … MBTsang, M.Colonna, HHWolter, …. (n/p, isospin diffusion, R(y), isoscaling, np flow, pi-/pi+) NSCL/MSU, GSI,FOPI

c), Theoretical reanalysis Problems: 1), can not describe the observable 2), can not self-consistent describe multi-obserevables

ImQMD05 (Improved QMD model developed at CIAE)  the mean fields acting on nucleon wavepackets are derived from Skyrme potential energy density functional potential energy density functional: EOS H=T+U+U_coul Surface symmetry energy term Detail of code: Zhang, et alPR C71 (05) , PR C74 (06) , PRC75,034615(07)., PL B664 (08) 145,

Parameters in U loc are obtained from standard Skyrme interactions parameters

 Isospin dependent nucleon-nucleon cross sections are adopted, the medium corrections are Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996) h depend on the beam energy

It describe the charge distribution, flow and stopping power well for the heavy ion collisions for Ebeam=30-400MeV, Zhang, Li, PRC71(2005)24606 Charge distribution data ImQMD Zhang, et.al., Nucl.Phys.Rev.2011

flow stopping Data: Residorf, PRL 92(2004) Zhang, Li, PRC74, Give our confidence to study the isospin effects from different symmetry energy case. Zhang, Li, PRC74,014602

The influence of  symmetry potential  Isospin dependence of In- medium NN cross section  Impact parameter  Cluster formation on heavy collision observables (DR(n/p), Ri) for Sn+Sn at50AMeV by ImQMD05.

The influence of different aspects on isospin sensitive observables (DR(n/p), Isospin diffusion) at E_beam=50AMeV  Symmetry potential The influence of medium correction The influence of  in-medium NN cross section

No isospin diffusion between symmetric systems Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy R i = 1 R i = -1 R i =(2X-X AA -X BB )/(X AA -X BB ) Isospin transport ratio In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium Theory: X is the , the isospin asymmetry of projectile residues Exp: X is the isoscaling parameter  (Tsang, PRL) There is linear relationship between  and , So, Ri(  )=Ri(  ) isospin diffusion DR(n/p) ratio DR(n/p)=R n/p (124)/R n/p (112) R n/p =Y(n)/Y(p)The yield ratio of emitted neutron to proton

The influence of the symmetry potential, in-medium NN cs on DR and Ri DR(n/p) with Ek>40MeV DR(n/p) and Ri sensitive to the density dependence of symmetry energy rather than in-medium NN cs for Sn+Sn at E/A=50MeV b=2fm b=6fm larger symmetry energy at subsaturation density leads to larger DR and smaller Ri

 Cluster emission Low intermediate energy HICs-> Multifragmentation  Impact parameters Experiment-> centrality, impact parameter smearing effect in exp. data

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 g i =0.5 calculation DR(n/p)=R n/p (124)/R n/p (112) Data from Famiano,PRL97, (2006) DR(n/p) with higher kinetic energy weakly depend on the impact parameters Y.Zhang, P.Danielewicz, et al, PLB664,145(2008) Zhang, et.al,2011

Zhang,, et.al., arXiv , cluster emission from neck region increase the values of Ri with heavy fragments. 1, Ri weakly depend on the impact parameters for b 5fm. Ri as a function of impact parameters 3), This phenomena can be performed.

Tsang/ Zhang/Danielewicz/Li/Lynch/Steiner et.al., PRL102(2009) 35AMeV, Sn+Sn Sun, et.al., PRC82(2010)051603R Constraints on the density dependence of symmetry energy with ImQMD05 Detailed comparison with data by varying g i Consistent c 2 analysis of these observables within ImQMD model provides with gamma_i=[0.45,0.95] ImQMD(05)

1)Around Fermi energy, the Ri and DR are strongly sensitive to the density dependence of symmetry energy rather than the in-medium cross section. 2)Cluster emission also play import roles on the HICs observables DR, Ri and its dependence on rapidity. 3)DR, Ri and Ry consistently support softer density dependence of symmetry energy. 3, Conclusions and discussion

Constraints on symmetry energy at subsaturatoin density S 0 ： the values of S(  ) energy at r 0 L ： the slope of S(  ) energy at r 0 K sym : the curvature of S(  ) energy at r 0 LWChen, BALi, et al,(Skin, Ri) Danielewicz, et.al PDR(Pb), A.Klimkiewicz Tsang,Zhang, et al.,PRL102(2009) ImQMD (DR, Ri, R 7 ) 50MeV/A, 35MeV/A, Liu(10) Mass Problem: Although overlap, but different in detail! S 0 ~31 ± 4 (MeV) L~60 ± 23 (MeV)

a), Probes is sensitive to the density dependence of symmetry energy (from theory) b), Experiment (Intermediate energy Heavy Ion Collisions) c), Theoretical reanalysis (n/p, isospin diffusion, pi-/pi+, n,p flow, t/He3,…) BALi, ZXLi, LWChen, QFLi, YXZhang, GCYong, … MBTsang, M.Colonna, HHWolter, …. (n/p, isospin diffusion, R(y), isoscaling, np flow) NSCL/MSU, GSI,FOPI d) theory, experiment

Thanks for your attention!