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Zhuxia Li (China Institute of Atomic Energy) Collaborators:

Probing the density dependence of the symmetry potential. Zhuxia Li (China Institute of Atomic Energy) Collaborators: Yinxun Zhang (CIAE), Qingfen Li (ITP), Ning Wang(ITP). Outline. 1) Equation of state for asymmetric nuclear matter

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Zhuxia Li (China Institute of Atomic Energy) Collaborators:

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

  2. Outline 1) Equation of state for asymmetric nuclear matter 2) Probing the density dependence of the symmetry potential at low densities 3) Probing the density dependence of the symmetry potential at high densities

  3. I. Equation of State for asymmetry 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) Esym(ρ)<0 when ρ>3ρ0 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 potential is highly requisite By nuclear structure: the accurate measurements of of Pb,Sn isovector giant resonance…

  7. By heavy ion collisions: The matter of various density and isospin asymmetry are produced---test the density dependence of the symmetry potential Find sensitive observables to the density dependence of symmetry potential Study dynamical effect of symmetry potential on the reaction mechanism

  8. II. Probing the symmetry potential at low densities Central collisions at intermediate energies： multifragmentation- isospin distillation in L-G phase transition

  9. Isoscaling effect (Tsang,et.al, PRL,2001) Nucl-ex/0406008

  10. Peripheral reaction ----Isospin diffusion α M.B.Tsang,et.al. PRL 92 (2004)

  11. Probing the equilibrium with respect to isospin sensitive observables in HIC The normalized proton counting number as function of rapidity. Rz=1, for Zr+Zr, Rz=-1, for Ru+Ru, Rz=0, for Zr+Ru and Ru+Zr, if equilib.is reached Results show protons are not from an equilibrium source and the reaction is half transparent Li, Li,PRC64(01)064612

  12. Probing the symmetry potential at low densities by peripheral HIC Products in peripheral collisions at Fermi energies ：Calculations are performed by means of ImQMD model (Wang,Li,et.al., PRC, 65(2002)064648, 69(2004)034608) nuclear potential energy density functional :

  13. 20 10 e (MeV) 0 ? -10 -20 0 1 2 u For low densities we take the density dependence of Symmetry potential: 1.0 0.8 0.6 0.4 0.2 0

  14. Density dependence of the mean field contributing from symmetry potential When > 0 neutrons are more bound for =0.5 than for stiff symmetry pot. When < 0 neutrons are less bound for =0.5 than for stiff symmetry pot. It is just opposite for protons

  15. Density dependence of chemical pot. ε is the energy density Esym-stiff. Esym-soft Cs=35MeV μn(ρ)-μp(ρ)=4Esym(ρ)δ

  16. neutrons move to the neck region faster than protons, neck area experiences weak compression, expansion and finally ruptures PLF and TLF are at normal density nucleons and light charged particles are emitted from neck directly influences the motion of nucleons towards to neck region influences the emission rate of the neutrons and protons

  17. mass and charge distribution

  18. 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

  19. The spectrum of N/Z ratio

  20. N/Z ratio of free nucleons as function of impact parameters for peripheral reactions of

  21. Yields of and EES model Ni/Zi ,N/Z ratio of particles at neck area (emission source)

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

  23. Soft-sym Stiff-sym exp 1.9 124Sn+86Kr 2.5 112Sn+86Kr 1.98 1.54 1.4 36Ar+58Ni

  24. Conclusions I(low densities) 1) The N/Z ratio of emitted nucleons is enhanced with soft symmetry potential, while the slope of N/Z ratio of free nucleons vs impact parameters is enhanced with stiff symmetry potential for peripheral reactions. 2) The yields of H3 ,He3 and the ratio depend on Esym(ρ) sensitively. The reducing slope of yield of H3 with impact parameters for peripheral reactions is very sensitive to the Esym(ρ) and asymmetry of the reaction system, while that of He3 is not.

  25. III. Study the density dependence of the symmetry potential at high density π-/π+ ratio is sensitive to the Esym(ρ) atρ>ρ0 B.A. Li, NPA 2002

  26. 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

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

  28. Probing the density dependence of symmetry potential by -/+ and Σ-/ Σ+ ratio by means of UrQMD-V1.3

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

  30. Symmetry potential for resonances (Δ++,+,0,-,N*) and ,Σ+-,0 For resonances: are determined by isospin C-G coef. in B*+N For Σ+-,0, assuming charge independence of the baryon-baryon interaction, in the linear approximation in y= (Z-N)/A V (Σ+-)=V0 (Σ+-)12V1 (Σ+-) y V1, Lane potential

  31. -/+ and Σ-/ Σ+ ratio by UrQMD with symmetry potential b a a 1.5AGeV b 2.5AGeV b 3.5AGeV a Stiff Esym(a) Soft Esym(b) Sensitity to Esym (ρ) reduces as energy increase for -/+

  32. At low energy case pions are produced mainly through  , the -/+ ratio is determined by n/ p.

  33. b N/Z|132Sn =1.64 b a b a a b a b b a a b a b b a a Red lines for soft-Esym and black lines for stiff-Esym

  34. 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+

  35. 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

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

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

  38. 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.

  39. 3) The ratio dependson the symmetry potential of in additionto those of particles which produce ’s. Therefore a more complicated situation appears for the ratio, a reversionis appeared from E= 1.5 AGeV to E=3.5 AGeV, which may provide a useful probe to obtain the information of Lane potential V1.

  40. Thanks for the patience

  41. II) In-Medium Nucleon-Nucleon Elastic Scattering cross Section The dynamics in heavy ion collisions at Fermi energies is dominated by both mean field and collision terms. The isospin dependence of two-body scattering cross sections and its medium correction plays an important role in the reaction dynamics. Empirically, the form of medium correction is taken as: σ=σ0 (1-αρ/ρ0), α is taken as a parameters and is isospin independent

  42. Our study is based on the formalism of the closed time Green’s function . With this approach, both mean field and two-body scattering cross sections can be obtained with the same effective interactions (self-consistently). The analytical expressions of the in-medium two-body scattering cross sections are obtained by computing the collisional self-energy part up to Born terms. Refs: Mao, Li, Zhuo, et.al, PRC.49(1994), Phys.lett. B327(1994)183, PRC53(1996), PRC55(1997)387, … Li, Li, Mao, PRC 64(2001)064612 Li, Li, PRC , accepted

  43. The effective Lagrangian density of density dependent relativistic hadron field theory: The coupling constants are of the functional of density Ref: PRC64(2001)034314 The energy density is:

  44. M*(x)=M0+ΣHσ(x)+ Σ Hδ(x) Mp Mn

  45. The Feynman diagrams for computing the in-medium nucleon-nucleon elastic scattering cross section (Mao,Li, et.al, PRC.49(1994), Li,Li,Mao, PRC 64(2001)064612)

  46. The contributions from σ and ω exchange σnp The isospin dependence of in-medium cross sections is contributed from ρ and δ meson σnn(pp) σnp/σnn(pp) σnp The density dependence of σnp, σnn(pp) at Yp=0.5 and Yp=0.3 σpp σnn

  47. σ-δ The contributions to σnn(pp), σnp from the ρ and δ related terms (total 7 terms) ωρ ωδ σρ There exist strong cancellation effect. The final results are the delicate balance between 7 terms σρ ωδ ωρ σρ

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