Constraining nuclear symmetry energy from high-energy heavy-ion

collisions

Zhao-Qing Feng (冯兆庆 )

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 Esym(ρ) in Nuclear Reactions B.A. Li, L.W. Chen, C.M. Ko, Phys. Rep. 464(2008) 113-281

Introduction

3

L.W. Chen, C.M. Ko, and B.A. Li PRC72,064309 (2005); PRC76, 054316 (2007)

4

Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(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)057901

momshloccoul UUUUU int

rr dloc

U Vloc

23/5

0

3/8

2

0

2

00

1

0

2

)(

)]([2212

potsym

pn

isosursur

Eg

gglocV

Evolution of baryons (nucleons and resonances )

Symmetry energy per nucleon in the LQMD model is derived from the Skyrme energy-density functional

with Cpot=38 MeV, a=37.7 MeV, b=-18.7 MeV which gives the Esym=31.5 MeV at =0=0.165

8

More clearly compared with other transport models, e.g., IBUU04, RBUU, SMF etc

2

00

3/22

2

2

3

23

1)(

ba

mEsym

Channels of kaon production near threshold

Energies:

B(N, ), K(K0, K+), Kb(Kb0,K-), Y(, -, 0, +)

BBBYK, BBBBKKb, BYK, BNKKb,

YNKb, NKbY, YNKbNN

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) 062501)

10

11

Evolution of nucleons, resonances and pions calculated by LQMD197Au+197Au, 1A GeV

-20 -10 0 10 20-10

-5

0

5

10

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15t=0 fm/c t=20 fm/c

-20 -10 0 10 20-10

-5

0

5

10t=10 fm/c

t=15 fm/c

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15t=25 fm/c

-20 -10 0 10 20-10

-5

0

5

10 neutron proton delta pion

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15t=30 fm/c

Time evolutions of pion, kaon and sigma in the reaction 197Au+197Au at 1.5A GeV by LQMD

Phys. Rev. C 82 (2010) 057901

12

Phenomenological anzatz for pion optical potential: PRC 35 (1987) 2107

Evolution of mesons (pions and kaons )is given by

0 2 4 6 80.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 2 4 6 8-6

-5

-4

-3

-2

-1

0

1.50

3.00

(m

)p (mc)

Re V

opt (

m)

p (mc)

13

14

J. Xu, C. M. Ko and Y. Oh, PRC 81 (2010) 024910

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

17

-/+ 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) 202301; NPA832 (2010) 88

20

Model of Di Toro group (RBUU) PRL97(2006)202301

stifferEsym(20)

IBUU04: PRL102(2009)062502

21

132Sn+124Sn

22

Comparison of calculated direct flow and the FOPI dataarXiv:1006.2459, Phys. Rev. C 82, 044615 (2010)

23

24

Anistropies of - production in 197Au+197Au at Elab=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