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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). - PowerPoint PPT Presentation
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060516-20Shanghai
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)
060516-20Shanghai
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
060516-20Shanghai
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:
060516-20Shanghai
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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22
22
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