Elliptic flow in intermediate energy HIC and n-n effective interaction and

1. Elliptic flow in intermediate energy HIC and n-n effective interaction and in-medium cross sections Zhuxia Li China Institute of Atomic Energy(CIAE),Beijingcollaborators:Yingxun Zhang(CIAE) Qingfeng Li(Frankfurt)

2. Outline • Introduction • Improved Quantum Molecular Dynamics • Elliptic flow in HICs from Fermi energy to • hundreds AMeV • 4) Further test of the in-medium n-n cross section • from nuclear stopping • 5) Summary

3. I. Introduction Motivation: 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

4. Fourier expansion of azimuth angle distribution of emitted particles Transverse flow (sideways deflection) ,<px>/A in-plane emission Elliptic flow, the comparison of in-plane to out-plane emission positive v2 , preference of in-plane emission negative v2, preference of out-plane emission

5. P.Danielewicz, Science298(2002)1592

6. Excitation function of elliptic flow in Au+Au by FOPI, INDRA and ALARDIN collaborations Phys.Letts.B 612(2005)612

7. Elliptic flow in HICs at intermediate energies Positive v2 Rotational motion(weak compresion) (MF dominant) Low energy x X Transition energy Z Negative v2 Expansion (strong compression) (n-n collisions become important) High energy Almond shaped overlap zone

8. HICs at energies tens- hundreds MeV per nucleon both MF and two- body collisions play role Elliptic flow at this energy region shows complex interplay among rotation, expansion and shadowing MF----effective interaction –EOS Two-body collision part---- medium effect on n-n cross sections

9. Extract information of EoS K=354MeV K=200MeV

10. 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

11. Full calculations: By means of the closed time path Green’s function technique based on effective Lagrangian: PRC64(2001)034314

12. Full calculations based on extended QHD model S1/2=2.0GeV Ein=0.252GeV S1/2 =1.97GeV Ein=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 with effective mass scaling

13. The density and temperature dependence of σnn,σpp,σnp for Y=0.3 Ek=10MeV Y=Z/A in-medium cross section increases with temperature Li,Li,PRC69(2004)17601

14. We extract the information of medium effect on n-n cross sections from experiments From elliptic flow From nuclear stopping Then compare it with various different

15. II. ImQMD model The motion of particles is described in 6-N dimensional phase space Each nucleon is represented by a wave packet Wang, Li, Wu, Phys.Rev.C65,064608(2002), Phys.Rev C69,024604（2003）, Phys.Rev C69,034608(2004) H

16. ImQMD improvemet (1) Nuclear potential energy density functional Version I Vsym +Vsursym V Wang,Li,et.al., PRC 65(2002)064648, 69(2004)034608)

17. Version II The potential energy density functional is taken from the Skyrme interaction directly

18. The relations between the parameters in ImQMD and Skyrme interaction

19. Pauliprincipal ImQMD Improvement (2) • Phase space occupation number constraint • system size dependent wave packet width Wang, Li, Wu, Phys.Rev.C65,064608(2002)

20. Charge distribution of products in HIC Zhang, Li, PRC71(2005)24606

21. Charge distribution of products Exp.data W. Trautmann and W.Reidorf

22. Elliptic flow in HICs at Fermi energies • to hundreds AMeV Effective interaction Skyrme interaction SKP, Skm*, SLy7, SIII In-medium cross section

24. dominated by MF transition energy (b/bmax=0.38) The harder EOS provides stronger pressure SIII most negative flow

25. test the in-medium cross section by changing MF dominate Expansion dominate collision part plays important role

26. System size dependence of the transition energies of elliptic flow =0.223

27. IV) Further test of the in-medium n-n cross sections from nuclear stopping FOPI experiments PRL 92(2004)232301 E(AMeV) Nuclear stopping is measured by variance of transverse y distribution variance of longitudinal y distribution Vartl=

28. Au+Au Eb=400AMeV b=1fm Vartlexp=0.85-0.9

29. SKP Vartlexp=0.85-0.9 PRL92(2004)232301 -1 +1 y0

30. Vartlexp~0.7 Nuclear stopping requires in-medium cross section depending on the relative momentum of two colliding nucleons , consistent with what learned from elliptic flow

31. V. Summary • 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. • 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 QHDmodel.

32. Thanks

33. Elliptic flow in HICs

35. D.Vautherin and D.M.Brink, Phys. Rev. C5 (1972) 626 同位旋不对称的势能密度 The improvements in ImQMD H with Skyrme force: