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Elliptic flow in intermediate energy HIC and n-n effective interaction and in-medium cross sections

Zhuxia Li China Institute of Atomic Energy(CIAE),Beijing

collaborators: Yingxun Zhang(CIAE) Qingfeng Li(Frankfurt)

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Outline

1) Introduction2) Improved Quantum Molecular Dynamics 3) Elliptic flow in HICs from Fermi energy to hundreds AMeV 4) Further test of the in-medium n-n cross section from nuclear stopping5) Summary

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Considerable progress has been made in determining the EOS of nuclear matter from HI reaction data.

A prominent role is played by collective flow among the available observables as it is most direct connected to the dynamical evolution of the reaction system. The study of collective flow can provide significant constraint to the the EOS of nuclear matter and medium effect

I. Introduction

Motivation:

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22

22

2yx

yx

pp

ppv

Transverse flow (sideways deflection) ,<px>/A in-plane emission

Elliptic flow, the comparison of in-plane to out-plane emission

Fourier expansion of azimuth angle distribution of emitted particles

positive v2 , preference of in-plane emissionnegative v2, preference of out-plane emission

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P.Danielewicz, Science298(2002)1592

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Excitation function of elliptic flow in Au+Au

by FOPI, INDRA and ALARDIN collaborations

Phys.Letts.B 612(2005)612

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Z

X

Elliptic flow in HICs at intermediate energies

22

22

2yx

yx

pp

ppv

Almond shaped overlap zone

Transition energy

Rotational motion(weak compresion) (MF dominant)

Expansion (strong compression)(n-n collisions become important)

Low energy

Positive v2

Negative v2

High energy

x

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HICs at energies tens- hundreds MeV per nucleonboth MF and two- body collisions play role

Elliptic flow at this energy region shows complex interplay among rotation, expansion and shadowing

MF----effective interaction –EOSTwo-body collision part---- medium effect on n-n cross sections

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K=354MeV

K=200MeV

Extract information of EoS

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Extract in-medium n-n scattering cross sections

The medium correction to n-n cross section has attracted a lot of attention

Phenomenological way

Effective mass scaling

Perstam,Gale,PRC65(02)64611

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PRC64(2001)034314

By means of the closed time path Green’s function technique based on effective Lagrangian:

Full calculations:

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S1/2=2.0GeVEin=0.252GeV

S1/2 =1.97GeVEin=0.189GeV

Li, Li, PRC 62(2002)14606

at low relative momentum, roughly is consistent with effective mass scaling at high relative momentum, is not consistent witheffective mass scaling

Full calculations based on extended QHD model

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The density and temperature dependence of σnn,σpp,σnp for Y=0.3 Ek=10MeV

Li,Li,PRC69(2004)17601

Y=Z/A

in-medium cross section increases with temperature

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We extract the information of medium effect on n-n cross sections from experiments

From elliptic flowFrom nuclear stopping

Then compare it with various different

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II. ImQMD modelThe motion of particles is described in 6-N dimensional phase space

Wang, Li, Wu, Phys.Rev.C65,064608(2002),Phys.Rev C69,024604 （ 2003 ） ,Phys.Rev C69,034608(2004)

Each nucleon is represented by a wave packet

H

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ImQMD improvemet (1)

Wang,Li,et.al., PRC 65(2002)064648, 69(2004)034608)

Nuclear potential energy density functional

Version I

Vsym + Vsursym

V

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Version II

The potential energy density functional is taken from the Skyrme interaction directly

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The relations between the parameters in ImQMD and Skyrme interaction

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• Phase space occupation number constraint

1ifPauli principal

• system size dependent wave packet width

Wang, Li, Wu, Phys.Rev.C65,064608(2002)

ImQMD Improvement (2)

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Charge distribution of products in HIC

Zhang, Li, PRC71(2005)24606

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Charge distribution of products

Exp.data W. Trautmann and W.Reidorf

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III) Elliptic flow in HICs at Fermi energies to hundreds AMeV

Effective interaction Skyrme interactionSKP, Skm*, SLy7, SIII

In-medium cross section

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transition energy

most negative flow

(b/bmax=0.38)

The harder EOSprovides stronger pressure

dominated by MF

SIII

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test the in-medium cross section by changing

Expansion dominatecollision part plays

important role

MF dominate

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System size dependence of the transition energies of elliptic flow

=0.223

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Nuclear stopping is measured by variance of transverse y distribution variance of longitudinal y distribution

Vartl=

FOPI experiments

IV) Further test of the in-medium n-n cross sections from nuclear stopping

PRL 92(2004)232301

E(AMeV)

6Z

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Vartlexp=0.85-0.9

Au+Au Eb=400AMeV b=1fm 6Z

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Vartlexp=0.85-0.9

y0-1 +1

SKP

PRL92(2004)232301

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Vartlexp~0.7

Nuclear stopping requires in-medium cross sectiondepending on the relative momentum of two collidingnucleons , consistent with what learned from elliptic flow

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1) From our study it is shown that Elliptic flow in intermediate energy HI collisions influenced by both the effective interaction and medium correction of n-n cross sections.

2) Skyrme int. corresponding to a soft EOS are required for elliptic flow , at sub-transition energies MF dominates and at energies higher than transition energies two-body collisions become very important

3) The in-medium cross sections ( ) should depend on relative momentum between two nucleons , which is in consistent with the prediction of theoretical calculations based on extended QHD model.

V. Summary

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Thanks

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2yx

yx

pp

ppv

Elliptic flow in HICs

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D.Vautherin and D.M.Brink, Phys. Rev. C5 (1972) 626

同位旋不对称的势能密度

H

with Skyrme force:

The improvements in ImQMD