1. 060516-20 Shanghai 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)

2. 060516-20 Shanghai Outline 1)Introduction 2)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 stopping 5) Summary

3. 060516-20 Shanghai 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:

4. 060516-20 Shanghai Transverse flow (sideways deflection), /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 v 2, preference of in-plane emission negative v 2, preference of out-plane emission

5. 060516-20 Shanghai P.Danielewicz, Science298(2002)1592

6. 060516-20 Shanghai Excitation function of elliptic flow in Au+Au by FOPI, INDRA and ALARDIN collaborations Phys.Letts.B 612(2005)612

7. 060516-20 Shanghai Z X Elliptic flow in HICs at intermediate energies Almond shaped overlap zone Transition energy Rotational motion(weak compresion) (MF dominant) Expansion (strong compression) (n-n collisions become important) Low energy Positive v 2 Negative v 2 High energy x

8. 060516-20 Shanghai 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. 060516-20 Shanghai K=354MeV K=200MeV Extract information of EoS

10. 060516-20 Shanghai 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. 060516-20 Shanghai PRC64(2001)034314 By means of the closed time path Green’s function technique based on effective Lagrangian: Full calculations:

12. 060516-20 Shanghai S 1/2 =2.0GeV E in =0.252GeV S 1/2 =1.97GeV E in =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 Full calculations based on extended QHD model

13. 060516-20 Shanghai The density and temperature dependence of σ nn, σ pp, σ np for Y=0.3 E k =10MeV Li,Li,PRC69(2004)17601 Y=Z/A in-medium cross section increases with temperature

14. 060516-20 Shanghai 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. 060516-20 Shanghai II. ImQMD model The 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

16. 060516-20 Shanghai ImQMD improvemet (1) Wang,Li,et.al., PRC 65(2002)064648, 69(2004)034608) Nuclear potential energy density functional Version I V sym + V sursym V

17. 060516-20 Shanghai Version II The potential energy density functional is taken from the Skyrme interaction directly

18. 060516-20 Shanghai The relations between the parameters in ImQMD and Skyrme interaction

19. 060516-20 Shanghai Phase space occupation number constraint Pauli principal system size dependent wave packet width Wang, Li, Wu, Phys.Rev.C65,064608(2002) ImQMD Improvement (2)

20. 060516-20 Shanghai Charge distribution of products in HIC Zhang, Li, PRC71(2005)24606

21. 060516-20 Shanghai Charge distribution of products Exp.data W. Trautmann and W.Reidorf

22. 060516-20 Shanghai III)Elliptic flow in HICs at Fermi energies to hundreds AMeV Effective interaction Skyrme interaction SKP, Skm*, SLy7, SIII In-medium cross section

23. 060516-20 Shanghai

24. 060516-20 Shanghai transition energy most negative flow (b/b max=0.38 ) The harder EOS provides stronger pressure dominated by MF SIII

25. 060516-20 Shanghai test the in-medium cross section by changing Expansion dominate collision part plays important role MF dominate

26. 060516-20 Shanghai System size dependence of the transition energies of elliptic flow =0.223

27. 060516-20 Shanghai 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)

28. 060516-20 Shanghai Vartl exp =0.85-0.9 Au+Au E b =400AMeV b=1fm

29. 060516-20 Shanghai Vartl exp =0.85-0.9 y0y0 +1 SKP PRL92(2004)232301

30. 060516-20 Shanghai Vartl exp ~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. 060516-20 Shanghai 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

32. 060516-20 Shanghai Thanks

33. 060516-20 Shanghai Elliptic flow in HICs

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35. 060516-20 Shanghai 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