Probing the Density Dependence of Symmetry Energy Term

1. Probing the density dependence of the symmetry energy term Zhuxia Li (China Institute of Atomic Energy) Collaborators: Yinxun Zhang (CIAE), Qingfen Li (FIAS), Ning Wang(CIAE)

2. Outline 1) Introduction 2) Improved Quantum Molecular Dynamics model 3) Probing the density dependence of the symmetry energy at subnormal and supra-normal densities

3. I. Intruduction EOS of asymmetric nuclear matter Empirical parabolic law: Esym(ρ)=E(ρ,neutron matter) -E(ρ,symmetric matter)

4. EOS for Asymmetric Nuclear Matter EOS of Neutron matter for 18 Skyrme Parameter sets ( B. Alex Brown, PRL85 5296) extreme variation is observed Other interactions such as Gogny,density dependent M3Y also give either positive or negative symmetry energies at high densities The sign of symmetry energy at ρ>3ρ0 is very uncertain. At ρ~0.5ρ0 Esym is variant. Even at normal density the values of Esym(symmetry energy coefficient) are different for different interactions.

5. The implication of the Esym(ρ) in astrophysics: • Nucleosynthesis in pre-supernova evolution of massive star • Mechanism of supernova explosion • Composition of protoneutron star • Cooling mechanism of protoneutron stars • Kaon condensation of neutron stars • Quark-hadron phase transition in neutron stars • Mass-radius correlation of neutron stars • Isospin separation instability and structure of neutron stars • Refs. H.A.Bethe, Rev.of Mod. Phys. 62(1990)801 • C.J. Pethick and D.G. Ravenhall, • Annu.Rev.Nucl.Part.Sci.85(95)429

6. Obtaining more accurate information of the symmetry energy term is highly requisite By nuclear structure: the accurate measurements of of Pb,Sn isovector giant resonance…

7. heavy ion collisions- unique means to study the density dependence of the symmetry energy The matter of various density and isospin asymmetry can be produced during reaction process Study dynamical effect of symmetry potential on the reaction mechanism Search for sensitive observables to the density dependence of symmetry potential Eventually, obtain the more accurate information of the symmetry energy term of EOS

8. the promising probes for the symmetry energy term at subnormal density: N/Z ratio of emitted nucleons ratio between the yields of 3H and 3He isospin fractionation isoscaling in multifragmantation proton differential elliptic flow neutron-proton transverse flow more… central or semi-central collisions B. A. Li B.T. Tsang L.W. Chen D.V. Chetty To obtain γ

9. the promising probes for the symmetry energy term at supra-normal density: B.A. Li, et.al, T.Gaitanos, et.al. Q.Li and Z.Li The ratios between negative and positive charged produced particles are enhanced for neutron-rich heavy ion collisions

10. Our recent work Study the effects of different forms of the density dependence of symmetry energy on peripheral HIC at intermediate energies (impact parameter dependence of the effects of symmetry energies) ImQMD model is applied A comprehensive study of the effects of different forms of the density dependence of the symmetry energy in a broad range of densities including subnormal and supra-normal densities UrQMD+Vsym is applied

11. II. Improved Quantum Molecular Denamics model (ImQMD) Wang,Li,et.al., PRC 65(2002)064648, 69(2004)034608) Nuclear potential energy density functional Version I Vsym +Vsursym

12. The energy density functional is taken from the mean field with Skyrme interaction directly Version II

13. The relations between the parameters in ImQMD and Skyrme interaction

15. Charge distribution of products in HIC

17. III) Probing the density dependence of the symmetry energy at subnormal and supra-normal densities 1) 112,124Sn+86Kr peripheral reactions @25AMeV G.A.Souliots, M.Veselsky, G.Chubarian, et.al., PR L. 91 022701(2003) 2) a comprehensive study of the effect of different forms of the symmetry energy on HIC at subnormal and supra-normal densities – to map out the density dependence of symmetry energy term in a broad range of densities

18. motion of protons and neutrons emission rate of protons and neutrons

19. 124Sn+86Kr peripheral reactions @25AMeV

20. emission time for neutrons and protons neutron

21. mass and charge distribution

22. Time evolution of N/Z ratio for particles at neck region Neutron skin effect N/Z increases with b matter at neck area is neutron -rich plateau

23. The spectrum of N/Z ratio

24. N/Z ratio of free nucleons as function of impact parameters for

25. Yields of3H and 3He as function of b soft stiff soft stiff

26. Soft-sym Stiff-sym exp 124Sn+86Kr 2.33 1.86 112Sn+86Kr 1.85 1.4 1.4 36Ar+58Ni central reactions

27. Conclusions I • Strong effect of symmetry potential on the slope of the N/Z ratio of free nucleons vs impact parameters in peripheral reactions is explored . The slope is strongly enhanced with stiff symmetry potential . • 2) The yield of 3H and the ratio Y(3H)/Y(3He) in peripheral reactions depend on Esym(ρ) strongly. The reducing slope of yield of 3H with impact parameters for peripheral reactions is very sensitive to the Esym(ρ) and isospin asymmetry of the reaction system, while that of 3Heis not.

28. In order to map out the density dependence of the symmetry energy at subnormal and supra-normal densities We make a simultaneous study of the effects of different symmetry energies at sub- and supra-normal densities. 208Pb+208Pb @0.4AGeV UrQMD+Vsym is adopted

29. Symmetry potential for resonances (Δ,N*) andΣ For resonances: are determined by isospin C-G coef. in B* For Σ+-,0, assuming charge independence of the baryon-baryon interaction V1 Lane potential

31. 1 2 3 4 T.Gaitanos,et.al.

33. Dmax=D23 1 3 4 2

35. Proton-neutron differential collective flow - differential elliptic flow 208Pb+208Pb @0.8AMeV@7-9fm T. Gaitanos,et. al. Nucl-th 0402041

36. and ratio by UrQMD + symmetry potential b a a 1.5AGeV b 2.5AGeV b 3.5AGeV a F1(a) Fa3(b) Sensitivity to Esym (ρ) reduces as energy increase for -/+

37. without the symmetry potential of Σ b (a) diff (b) b a a diff similar with -/+

38. Conclusion II we have investigated the influence of different forms of symmetry energies on various observables proposed to be sensitive to the symmetry energy at subnormal and superanomal densities. We have shown that the differences between the values of observables predicted with different symmetry potentials has a close correspondence with the different behavior of the density dependence of the symmetry energies at certain region of densities. It will help us to map out the density dependence of the symmetry energy term at a broad densities and to extract the knowledge of the isospin dependent part of the effective interaction.

39. Thanks for the patience

40. B.A. Li, NPA,2002 Stiff symmetry potential Soft symmetry potential The density dependence of Esym strongly influence the structure of neutron star Direct URCL limit Proton fraction 1/9

41. π-/π+ ratio is sensitive to the Esym atρ>ρ0 B.A. Li, NPA 2002

42. The production rate of and at different densities UrQMD without symmetry potential

45. At low energy case pions are produced mainly through , the ratio is determined by the ratio of N/P.

46. Δ+ +,Δ+,Δ0 ,Δ– production strongly depends on ρn/ρp For E~1AGeV or less pions are mainly produced by Δ therefore π-/π+~(N/Z)2 For E>>1AGeV many channels open. The situation becomes more complicated Σ-/ Σ+ is more complicated than π-/π+

47. Σ is baryon, as soon as it is produced it will be under of the mean field of nuclear matter. The ratio of Σ+/Σ- therefore is also depends on the symmetry potential of Σ in nuclear matter, in addition to those of particles which produce Σ

48. without the symmetry potential of Σ Soft-sym b a b a Stiff-sym similar with -/+

49. The effect of the symmetry potential of Σ in nuclear matter can not be neglected! The strength of this effect depends on V1

50. Conclusions II(high densities) • A strong dependence of the ratios of-/+ and • Σ -/ Σ+on Esym(ρ)which provide good means for study Esym at ρ> ρ0 . • 2) The ratio of -/+  n/ p for E=1.5 AGeV case but • not 3.5 AGeV case. The sensitivity of -/+ ratio to • Esym(ρ) reduced as energy increases.