Institute of Modern Physics, CAS Probing the high-density behavior of the symmetry energy from pion emission in heavy-ion collisions Zhao-Qing Feng (冯兆庆) Institute of Modern Physics, CAS (中国科学院近代物理研究所，兰州) Aug 22-25 IWND09

Outline Motivation for investigating symmetry energy in heavy-ion collisions Improved isospin dependent quantum molecular dynamics (ImIQMD) model Pion emission in heavy-ion collisions in 1A GeV region as probes of symmetry energy Summary Aug 22-25 IWND09

Aug 22-25 IWND09

Symmetry energy per nucleon: L.W. Chen, C.M. Ko, and B.A. Li PRC72,064309 (2005); PRC76, 054316 (2007) Aug 22-25 IWND09 4

Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003) BHF Aug 22-25 IWND09

I. Vidana et al., arXiv: 0907.1165 Aug 22-25 IWND09

Promising probes of the Esym(ρ) in Nuclear Reactions B. A. Li, L. W Promising probes of the Esym(ρ) in Nuclear Reactions B.A. Li, L.W. Chen, C.M. Ko, Phys.Rep.464(2008) 113-281, L.W. Chen’s Talk in Lanzhou Aug 2009 Aug 22-25 IWND09

Improved isospin dependent quantum molecular dynamics model (ImIQMD or IQMD08) ‘Quantum molecular dynamics model’ (QMD) by Aichelin et al., Phys. Rep 202 (1991) 233, PRL 58 (1987) 1926 Based on isospin dependent quantum molecular dynamics model (IQMD, Refs: L.W. Chen et al.,PRC58(1998)2283, PLB459(1999)21; F.S. Zhang et al., PRC60(1999)064604) Potential energy terms (two and three body terms, surface and surface symmetry terms, effective mass, symmetry energy term) in ImIQMD model are derived from Skyrme energy density functional Nucleon’s fermionic nature is embodied by using a phase space constraint method Shell effect is considered by a phenomenological approach in description of heavy-ion fusion reactions (Z.Q. Feng et al., NPA750(2005)232, NPA802(2008)91) Inelastic channels in nucleon-nucleon collisions are also included, such as NNN(1232), NNNN*(1440) Experimental elastic and inelastic cross sections are parameterized in the ImIQMD model Aug 22-25 IWND09

Simple introduction of ImIQMD model Time evolutions for baryons: Aug 22-25 IWND09

Symmetry energy in ImIQMD model from Skyrme energy-density functional Also expressed as with s=0.5 (soft), s=1. (linear, IQMD) and s=2. (hard) with Csym=32 MeV Time evolutions for pions: Reaction channels for inelastic nucleon-nucleon collisions Aug 22-25 IWND09

NN elastic and inelastic cross sections (Chin. Phys. Lett Aug 22-25 IWND09

ImIQMD parameters with and without momentum dependent (Z. -Q ImIQMD parameters with and without momentum dependent (Z.-Q. Feng et al., Nucl.Phys.A802(2008)91, Chin.Phys.Lett.26(2009)062501) Parameters with momentum dependent with =1.57 MeV and =500 c2/GeV2 (PRL 58 (1987) 1926) Aug 22-25 IWND09

Aug 22-25 IWND09

Pion as probes of symmetry energy at supra-saturation density Aug 22-25 IWND09

Transverse momentum distribution with parameter SLy6 but soft and hard symmetry energy Aug 22-25 IWND09

-/+ at different Skyrme parameters and stiffness of the symmetry energy SLy6 Aug 22-25 IWND09

ImIQMD: arXiv:0904.2990 IBUU04: PRL102(2009)062502 Aug 22-25 IWND09

UrQMD: W. Trautmann et al., arXiv:0907.2822 Model of Di Toro group PRL97(2006)202301 stiffer Esym(20) Aug 22-25 IWND09

Transport theories for heavy-ion collisions in the 1 A GeV region J.Phys.G 31 (2005) S741-757 Transport theories for heavy-ion collisions in the 1 A GeV region Aug 22-25 IWND09

Summary Symmetry energy at supra-saturation density is investigated by analyzing the -/+ ratios in heavy-ion collisions within the framework of the ImIQMD model Preliminary results compared with the measured data by the FOPI collaboration favor a hard symmetry energy of the potential term proportional to (/0)s with s=2 High-density behavior of the symmetry energy is still an open problem, which should be supplemented by more experimental data. Different models (IBUU04, ImIQMD, UrQMD, etc) or observables predict different stiffness of the symmetry energy. A consistent results of various models should be required. Aug 22-25 IWND09