Aug 22-25 IWND09 1

Probing the high-density behavior of the symmetry energy from pion emission in heav

y-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 2

Outline

Motivation for investigating symmetry ener

gy in heavy-ion collisions

Improved isospin dependent quantum mole

cular dynamics (ImIQMD) model

Pion emission in heavy-ion collisions in 1A

GeV region as probes of symmetry energy

Summary

Aug 22-25 IWND09 3

Aug 22-25 IWND09 4

)0,()1,(),(

2

1)(

0

2

2

EEE

EsymSymmetry energy per nucleon:

L.W. Chen, C.M. Ko, and B.A. LiPRC72,064309 (2005); PRC76, 054316 (2007)

Aug 22-25 IWND09 5

Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003)

BHF

Aug 22-25 IWND09 6

I. Vidana et al., arXiv: 0907.1165

Aug 22-25 IWND09 7

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

At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/3He ratio Hard photon production

Towards high densities reachable at CSR/China, FAIR/GSI, RIKEN, GANIL and, FRIB (高密度行为) π -/π + ratio, K+/K0 ratio? Neutron-proton differential transverse flow n/p ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta n/p ratio of squeeze-out emission

Aug 22-25 IWND09 8

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 NNN(1232), NNNN*(1440)

Experimental elastic and inelastic cross sections are parameterized in the ImIQMD model

Aug 22-25 IWND09 9

Simple introduction of ImIQMD model

Time evolutions for baryons:

Aug 22-25 IWND09 10

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)

Time evolutions for pions:

Reaction channels for inelastic nucleon-nucleon collisions

2

00

0

2

00

22

31

2

22

3

212

LLktt

Cg

LL

gU

jisym

iij

j

ijjziz

sym

iij

j

ij

i

ij

ijj

jisur

iij

j iij

j

ijijloc

rr

rr

with Csym=32 MeV

Aug 22-25 IWND09 11

NN elastic and inelastic cross sections (Chin.Phys.Lett.26(2009)062501)

Aug 22-25 IWND09 12

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 13

Aug 22-25 IWND09 14

Pion as probes of symmetry energy at supra-saturation density

Aug 22-25 IWND09 15

Transverse momentum distribution with parameter SLy6 but soft and hard symmetry energy

Aug 22-25 IWND09 16

-/+ at different Skyrme parameters and stiffness of the

symmetry energy

SLy6

Aug 22-25 IWND09 17

ImIQMD: arXiv:0904.2990

IBUU04: PRL102(2009)062502

Aug 22-25 IWND09 18

Model of Di Toro group PRL97(2006)202301

UrQMD: W. Trautmann et al., arXiv:0907.2822

stifferEsym(20)

Aug 22-25 IWND09 19

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

Aug 22-25 IWND09 20

Summary Symmetry energy at supra-saturation density is investigated by

analyzing the -/+ ratios in heavy-ion collisions within the fram

ework of the ImIQMD model

Preliminary results compared with the measured data by the F

OPI 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 p

roblem, which should be supplemented by more experimental d

ata. Different models (IBUU04, ImIQMD, UrQMD, etc) or observa

bles predict different stiffness of the symmetry energy. A consi

stent results of various models should be required.