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

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

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

CCAST EOS for Asymmetric Nuclear Matter EOS of Neutron matter for 18 Skyrme Parameter sets ( B. Alex Brown, PRL ) 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.

CCAST The implication of the E sym (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

CCAST 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…

CCAST 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 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

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

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

CCAST 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+V sym is applied 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 Our recent work

CCAST 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 V sym + V sursym

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

CCAST The relations between the parameters in ImQMD and Skyrme interaction

CCAST

CCAST Charge distribution of products in HIC

CCAST

CCAST III) Probing the density dependence of the symmetry energy at subnormal and supra-normal densities 1) 112,124 Sn+ 86 Kr peripheral 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 G.A.Souliots, M.Veselsky, G.Chubarian, et.al., PR L (2003)

CCAST emission rate of protons and neutrons motion of protons and neutrons

CCAST 124 Sn+ 86 Kr peripheral

CCAST emission time for neutrons and protons neutron

CCAST mass and charge distribution

CCAST 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

CCAST The spectrum of N/Z ratio

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

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

CCAST 124 Sn+ 86 Kr 112 Sn+ 86 Kr Soft-symStiff-sym Ar+ 58 Ni exp 1.4 central reactions

CCAST Conclusions I 1)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 3 H and the ratio Y( 3 H)/Y( 3 He) in peripheral reactions depend on E sym (ρ) strongly. The reducing slope of yield of 3 H with impact parameters for peripheral reactions is very sensitive to the E sym (ρ) and isospin asymmetry of the reaction system, while that of 3 He is not.

CCAST 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. 208 Pb+ 208 UrQMD+Vsym is adopted

CCAST Symmetry potential for resonances (Δ,N * ) and Σ For resonances: are determined by isospin C-G coef. in B * For Σ +-,0, assuming charge independence of the baryon-baryon interaction V 1 Lane potential

CCAST

CCAST T.Gaitanos,et.al.

CCAST

CCAST D max =D

CCAST

CCAST 208Pb+208Pb - differential elliptic flow Proton-neutron differential collective flow T. Gaitanos,et. al. Nucl-th

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

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

CCAST 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.

CCAST Thanks for the patience

CCAST 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

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

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

CCAST

CCAST

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

CCAST 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 +

CCAST 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

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

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

CCAST 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.

CCAST 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.

CCAST Thanks for the patience

CCAST 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

CCAST 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

CCAST 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

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

CCAST ( 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

CCAST 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)

CCAST 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

CCAST 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

CCAST 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

CCAST 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

CCAST 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

CCAST 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