Constraining nuclear symmetry energy from high-energy heavy-ion collisions Zhao-Qing Feng ( ) Institute of Modern Physics, Lanzhou, Chinese Academy of Sciences (CAS)

Outline Introduction Lanzhou Quantum Molecular Dynamics (LQMD) model Particle production in LQMD model Probing equation of state (EOS) and symmetry energy by heavy-ion collisions in the region of 1 A GeV Summary 2

Promising probes of the E sym (ρ) in Nuclear Reactions B.A. Li, L.W. Chen, C.M. Ko, Phys. Rep. 464(2008) Introduction 3

L.W. Chen, C.M. Ko, and B.A. Li PRC72, (2005); PRC76, (2007) 4 Z.H. Li et al., PRC74, (2006) Dieperink et al., PRC68, (2003)

IBUU04 Different symmetry energies used in transport models 5 LQMD

Lanzhou-Quantum-Molecular- Dynamics (LQMD) project Dynamics of low-energy heavy-ion collisions (dynamical interaction potential, barrier distribution, neck dynamics, fusion/caption excitation functions etc) Isospin physics at intermediate energies (constraining symmetry energy at sub or supra saturation densities in HICs) Medium effects in heavy-ion collisions and proton induced reactions (probing the in-medium NN elastic and inelastic cross sections, properties of resonances (1232), N*(1440), N*(1535)) and mesons such as, kaons, ) Dilepton production (e + e - ) at near threshold energies in heavy-ion collisions and proton induced reactions. 6

Lanzhou Quantum Molecular Dynamics (LQMD) 7 Refs: NPA750(2005)232, NPA802(2008)91, PRC80(2009)037601, PLB683(2010)140, PRC82(2010)044615, 82(2010) Evolution of baryons (nucleons and resonances )

Symmetry energy per nucleon in the LQMD model is derived from the Skyrme energy-density functional with C pot =38 MeV, a=37.7 MeV, b=-18.7 MeV which gives the E sym =31.5 MeV at = 0 = More clearly compared with other transport models, e.g., IBUU04, RBUU, SMF etc

Channels of kaon production near threshold Energies: B(N, ), K(K 0, K + ), Kb(Kb 0,K - ), Y(, -, 0, + ) BB BYK, BB BBKKb, B YK, B NKKb, Y NKb, NKb Y, YN KbNN Reaction channels for pion production: (1232), N*(1440), N*(1535) 9

NN elastic and inelastic cross sections (Z.-Q. Feng and G.-M. Jin, Chin.Phys.Lett. 26 (2009) ) 10

11 Evolution of nucleons, resonances and pions calculated by LQMD 197 Au+ 197 Au, 1A GeV

Time evolutions of pion, kaon and sigma in the reaction 197 Au+ 197 Au at 1.5A GeV by LQMD Phys. Rev. C 82 (2010)

Phenomenological anzatz for pion optical potential: PRC 35 (1987) 2107 Evolution of mesons (pions and kaons )is given by 13

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J. Xu, C. M. Ko and Y. Oh, PRC 81 (2010) Influence of pion optical potential on the - / + yields in the 197Au+197Au reaction 15

Probing symmetry energy by heavy-ion collisions in the region of 1 A GeV 16

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-/ + as a probe of the symmetry energy at supra-saturation densities (Z.-Q. Feng, G.-M. Jin, Phys. Lett. B 683 (2010) 140) 18

19 LQMD: Phys. Lett. B 683 (2010) 140 IBUU04: PRL102(2009)062502

RBUU: PRL97 (2006) ; NPA832 (2010) 88 20

Model of Di Toro group (RBUU) PRL97(2006) stiffer E sym (2 0 ) IBUU04: PRL102(2009)

132 Sn+ 124 Sn 22

Comparison of calculated direct flow and the FOPI data arXiv: , Phys. Rev. C 82, (2010) 23

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Anistropies of - production in 197 Au+ 197 Au at E lab =1.5 A GeV 25

Summary Dynamics of meson productions (pions, kaons) in the 1A GeV region is described in LQMD model. Pion flows and in-medium effects are discussed. Nuclear symmetry energy at supra-saturation densities is investigated by LQMD model. Preliminary results support a hard symmetry energy at high densities close to experimental data. 26