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

Weihai 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

Weihai I. Equation of State for asymmetry nuclear matter Empirical parabolic law: E sym (ρ)=E(ρ,neutron matter) -E(ρ,symmetric matter)

Weihai EOS for Asymmetric Nuclear Matter EOS of Neutron matter for 18 Skyrme Parameter sets ( B. Alex Brown, PRL )  Esym(ρ) 3ρ 0 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>3ρ 0 is very uncertain. At ρ~0.5ρ 0 Esym is variant. Even at normal density the values of Esym(symmetry energy coefficient) are different for different interactions.

Weihai The implication of the Esym(ρ) in astrophysics: a)Nucleosynthesis in pre-supernova evolution of massive star b)Mechanism of supernova explosion c)Composition of protoneutron star d)Cooling mechanism of protoneutron stars e)Kaon condensation of neutron stars f)Quark-hadron phase transition in neutron stars g)Mass-radius correlation of neutron stars h)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

Weihai Obtaining more accurate information of the symmetry potential is highly requisite By nuclear structure: the accurate measurements of of Pb,Sn isovector giant resonance…

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

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

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

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

Weihai 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

Weihai 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 :

Weihai e (MeV) u ? For low densities we take the density dependence of Symmetry potential:

Weihai 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

Weihai Density dependence of chemical pot. Cs=35MeV Esym-stiff. Esym-soft ε is the energy density μ n (ρ)-μ p (ρ)=4Esym(ρ)δ

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Weihai 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

Weihai mass and charge distribution

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

Weihai The spectrum of N/Z ratio

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

Weihai Yields of and EES model N i /Z i, N/Z ratio of particles at neck area (emission source)

Weihai Yields of 3H and 3He as function of b stiff soft stiff soft

Weihai 124Sn+86Kr 112Sn+86Kr Soft-symStiff-sym Ar+58Ni exp 1.4

Weihai 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 H 3,He 3 and the ratio depend on Esym(ρ) sensitively. The reducing slope of yield of H 3 with impact parameters for peripheral reactions is very sensitive to the Esym(ρ) and asymmetry of the reaction system, while that of He 3 is not.

Weihai III. Study the density dependence of the symmetry potential at high density π - /π + ratio is sensitive to the Esym(ρ) at ρ>ρ 0 B.A. Li, NPA 2002

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

Weihai B.A. Li, NPA 2002 π - /π + ratio is sensitive to the Esym at ρ>ρ 0

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

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

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Weihai 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 +- )=V 0 (Σ +- )  1  2V 1 (Σ +- ) y V 1, Lane potential

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

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

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

Weihai Δ + +, Δ +, Δ 0, Δ – production strongly depends on ρ n /ρ p 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 +

Weihai 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

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

Weihai The effect of the symmetry potential of Σ in nuclear matter can not be neglected! The strength of this effect depends on V 1

Weihai Conclusions II(high densities) 1)A strong dependence of the ratios of  - /  + and Σ - / Σ + on Esym(ρ) which provide good means for study Esym at ρ> ρ 0. 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.

Weihai 3) The ratio depends on the symmetry potential of in addition to those of particles which produce ’s. Therefore a more complicated situation appears for the ratio, a reversion is appeared from E= 1.5 AGeV to E=3.5 AGeV, which may provide a useful probe to obtain the information of Lane potential V 1.

Weihai Thanks for the patience

Weihai 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= σ 0 (1-αρ/ρ 0 ), α is taken as a parameters and is isospin independent

Weihai 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) Li, Li, PRC, accepted

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

Weihai M*(x)=M 0 +Σ Hσ (x)+ Σ Hδ (x) MpMp MnMn

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

Weihai The isospin dependence of in-medium cross sections is contributed from ρ and δ meson The contributions from σ and ω exchange The density dependence of σ np, σ nn(pp) at Yp=0.5 and Yp=0.3 σ np σ nn(pp) σ np σ pp σ nn σ np /σ nn(pp)

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

Weihai The density and temperature dependence of σ nn, σ pp, σ np for Y=0.3 E k =10MeV Clear isospin dependence for in-medium cross section is seen. The density dependence is stronger than temperature dependence. The isospin dependence of cross section will influence the reaction dynamics strongly. Y=Z/A

Weihai III. Isospin effect in HIC Multifragmentation multifragmentation in intermediate HIC relating to possible liquid-gas phase transition (M.Fisher,Physics(N.Y.)3(1967)255,PRL88,042701,PRL88,022701, PRC52,2072,…) We study multifragmentation through central collisions in intermediate HIC. isospin distillation,isoscaling effect, ….. N/Z of free nucleons, IMF, light charged particles strongly depends on the symmetry energy Flow effects neutron,proton flow, light charged particle flow, differential flow,… (various kind flow) Probing the density dependence of Esym at ρ<ρ 0

Weihai The momentum distribution of N np of nucl. and IMF a)The effect of Cs on N np of nucleons is more pronounced at large momentum and that of  is more pronounced at small momentum (because nucleons with large momentum mainly emitted at early time and that of small momentum emitted at later stage). b) Nnp(IMF) for  =0.5 enhances at p/p proj <0.25 (Coulomb effect) and at large p/p proj >1.0 ( density dependence of symmetry pot. ?) comparing with sym- stiff case. P/P proj

Weihai 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

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