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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. 利用重离子碰撞确定对称能密度依赖形式. 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). 10 月 27 日 广西 桂林. Outline. Symmetry energy Constraining the symmetry energy with HICs ImQMD05 the influence of symmetry potential In-medium NN cross section

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利用重离子碰撞确定对称能密度依赖形式

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  1. 核物理前沿热点问题研讨会 利用重离子碰撞确定对称能密度依赖形式 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) 10月27日 广西 桂林

  2. Outline • Symmetry energy • 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 • Conclusions and discussion

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

  4. S(r) (MeV) • Isospin asymmetric nuclear Equation of State 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, …. Symmetry energy S(r) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetric EOS. However, S(r) uncertainty

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

  6. 2, Constraining the symmetry energy with HICs a), Probes is sensitive to the density dependence of symmetry energy (from theory) (n/p, isospin diffusion, pi-/pi+, n,p flow, t/He3,…) BALi, ZXLi, LWChen, QFLi, YXZhang, GCYong, … MBTsang, M.Colonna, HHWolter, …. b), Experiment (Intermediate energy Heavy Ion Collisions) (n/p, isospin diffusion, R(y), isoscaling, np flow, pi-/pi+) NSCL/MSU, GSI,FOPI

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

  8. ImQMD05 (Improved QMD model developed at CIAE) Detail of code: Zhang, et alPR C71 (05) 024604, PR C74 (06) 014602, PRC75,034615(07)., PL B664 (08) 145, • the mean fields acting on nucleon wavepackets are derived fromSkyrme potential energy density functional H=T+U+U_coul EOS potential energy density functional: Surface symmetry energy term

  9. Parameters in Uloc are obtained from standard Skyrme interactionsparameters

  10. 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

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

  12. Zhang, Li, PRC74,014602 flow stopping Zhang, Li, PRC74,014602 Data: Residorf, PRL 92(2004)232301 Give our confidence to study the isospin effects from different symmetry energy case.

  13. 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.

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

  15. 124 112 Ri = -1 124 112 124 112 Ri = 1 DR(n/p) ratio Rn/p=Y(n)/Y(p) The yield ratio of emitted neutron to proton DR(n/p)=Rn/p(124)/Rn/p(112) isospin diffusion No isospin diffusion between symmetric systems Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy. Isospin transport ratio In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium Ri=(2X-XAA-XBB)/(XAA-XBB) Theory: X is the d, the isospin asymmetry of projectile residues Exp: X is the isoscaling parameter a (Tsang, PRL) There is linear relationship between d and a, So, Ri(d)=Ri(a)

  16. The influence of the symmetry potential, in-medium NN cs on DR and Ri DR(n/p) with Ek>40MeV b=2fm b=6fm • larger symmetry energy at subsaturation density leads to larger DR and smaller Ri • 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

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

  18. DR(n/p)=Rn/p(124)/Rn/p(112) Y.Zhang, P.Danielewicz, et al, PLB664,145(2008) Data from Famiano, PRL97, 052701(2006) Over the whole energy range for both free and coalescence-invariant DR(n/p) the data seem closer to the gi=0.5 calculation Significant cluster and sequential decay effects are at low energy! Zhang, et.al,2011 DR(n/p) with higher kinetic energy weakly depend on the impact parameters

  19. Ri as a function of impact parameters 1, Ri weakly depend on the impact parameters for b<5fm; increase with b for b>5fm. Zhang,, et.al., arXiv.1009.1928 2, cluster emission from neck region increase the values of Ri with heavy fragments. 3), This phenomena can be performed.

  20. Tsang/ Zhang/Danielewicz/Li/Lynch/Steiner et.al., PRL102(2009) Constraints on the density dependence of symmetry energy with ImQMD05 Sun, et.al., PRC82(2010)051603R Detailed comparison with data by varying gi 35AMeV, Sn+Sn Consistent c2 analysis of these observables within ImQMD model provides ImQMD(05) with gamma_i=[0.45,0.95]

  21. 3, Conclusions and discussion Around Fermi energy, the Ri and DR are strongly sensitive to the density dependence of symmetry energy rather than the in-medium cross section. Cluster emission also play import roles on the HICs observables DR, Ri and its dependence on rapidity. DR, Ri and Ry consistently support softer density dependence of symmetry energy.

  22. Tsang,Zhang, et al.,PRL102(2009) • Constraints on symmetry energy at subsaturatoin density ImQMD (DR, Ri, R7) 50MeV/A, 35MeV/A, Liu(10) Mass Danielewicz, et.al S0：the values of S(r) energy at r0 L： the slope of S(r) energy at r0 Ksym: the curvature of S(r) energy at r0 S0~31 ± 4 (MeV) L~60 ± 23 (MeV) PDR(Pb), A.Klimkiewicz Problem: Although overlap, but different in detail! LWChen, BALi, et al,(Skin, Ri)

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

  24. Thanks for your attention!

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