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Yu-Gang Ma Shanghai INstitute of Applied Physics, Chinese Academy of Sciences （ SINAP ， CAS ）

Unified description of nuclear stopping in central heavy-ion collisions from 10 A MeV to 1.2 A GeV. Yu-Gang Ma Shanghai INstitute of Applied Physics, Chinese Academy of Sciences （ SINAP ， CAS ） Collaborated with Guo-Qiang Zhang, Xi-Guang Cao, De-Qing Fang, Cheng-Long Zhou et al.

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Yu-Gang Ma Shanghai INstitute of Applied Physics, Chinese Academy of Sciences （ SINAP ， CAS ）

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  1. Unified description of nuclear stopping in central heavy-ion collisions from 10A MeV to 1.2A GeV Yu-Gang Ma Shanghai INstitute of Applied Physics, Chinese Academy of Sciences（SINAP，CAS） Collaborated with Guo-Qiang Zhang, Xi-Guang Cao, De-Qing Fang, Cheng-Long Zhou et al. Comparison of the IQMD-simulations of heavy ion collisions with experimental data of INDRA&FOPI Third International Conference on Nuclear Fragmentation From Basic Research to Applications October 2 - 9, 2011, Kemer (Antalya), Turkey NUFRA2011 Turkey

  2. Motivations and outline Motivations: Constrain the properties of nuclear matter • NN cross-section from nuclear stopping • Nuclear EOS from nuclear stopping Study of transport phenomena in central HIC • Multifragmentation or the other? • Equilibrium stage being reached? Outline: Background of nuclear stopping studies • Nuclear EOS, Equilibrium • INDRA Collaboration: Near Fermi energy • FOPI Collaboration: 102A MeV ~ A GeV Compare with IQMD • Describe nuclear stopping in different phase space • Stopping at event level and fragment level NUFRA2011 Turkey

  3. Nuclear EOS From GMR ρ~ρ0 Giant Monopole Resonance K0=231±5 MeV soft EOS! D. H. Youngblood, H. L. Clark, and Y.-W. Lui, Phys. Rev. Lett. 82, 691 (1999) NUFRA2011 Turkey

  4. Nuclear EOS Kaon production 1ρ0< ρ < 3ρ0 A soft EOS is favoured! J. Aichelin and C. M. Ko, PRL55, 2661 (1985) C. Fuchs et al, PRL86, 197(2001) C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, 012302 (2006) NUFRA2011 Turkey

  5. Nuclear EOS from flows 1.5ρ0< ρ < 7ρ0 Both in-plane flow and out-of-plane flow favor softer EOS (K~300MeV). Danielewicz, P.; Lacey, R. & Lynch, W. G. Science, 2002, 298, 1592-1596 NUFRA2011 Turkey

  6. stopping and flow FOPI experiment Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, 232301 Andronic, A et al. Eur. Phys. J., 2006, A30, 31-46 The ratio of the transverse over longitudinal variances; vartl1, full stopping, equilibration Scaled directed flow Left: pxdir @ b=5 fm (b/bmax=0.38) Right: yt and yl @b<2 fm ( b/bmax <0.15) The EoS is a relation between pressure and density, it is understandable that the stopping & flow are related to the EoS: flow is generated by pressure gradients established in compressed matter, while the achieved density is connected to the degree of stopping. NUFRA2011 Turkey

  7. stopping and flow FOPI experiment Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, 232301 Andronic, A et al. Eur. Phys. J., 2006, A30, 31-46 • Peak at 400MeV/u for vartl & flow • pxdir vs stopping: strong linear correl. • Size dependent A strong correlation exists between the stopping, measured in central collisions and the directed flow measured at impact parameters where it is maximal NUFRA2011 Turkey

  8. EOS from stopping in central HIC? pt Dynamical Equilibrium? pz Nuclear Stopping pt Isospin Equilibrium? pz Isospin tracing Isospin diffusion/transparency Multifragmentation? EOS from nuclear stopping? NUFRA2011 Turkey

  9. Nuclear stopping in Momentum moment pt Alternative definition on nuclear stopping: pz Qzz0, full stopping, equilibration energy dependent centrality dependent size dependent Bauer, W. Phys. Rev. Lett., 1988, 61, 2534-2537 NUFRA2011 Turkey

  10. More works T. Gaitanos et al., Phys. Lett. B595, 209 (2004). stopping, isospin equilibration T. Gaitanos et al., Phys. Lett. B 609,241 (2005) . stopping, flow, viscosity, NN K. Zbiri et al., Phys. Rev. C75, 034612 (2007). BQMD FOPI Fu, F. et al. Phys. Lett., B666, 359-363 (2008). stopping, compression, radial flow P. Danielewicz et al., AIP Conf. Proc. 1128, 104 (2009). BUU viscosity, NN X. G. Cao et al., Phys. Rev. C 81, 061603(R) (2010). Deformed nuclei, stopping, flow B.B. Back, et al., E917 Collaboration, Phys. Rev. Lett. 86, 1970(2001) AGS net-proton H. Appelshäuser, et al., NA49 Collaboration, Phys. Rev. Lett. 82,2471 (1999) SPS net-proton .... .... • No full Equilibration! • Low energy? • Why? • EOS from stopping? AGS ? SPS Reisdorf, W. et al., Nucl. Phys., 2010, A848, 366-427 NUFRA2011 Turkey

  11. INDRA experiment: stopping near Fermi energy Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701 NUFRA2011 Turkey

  12. Liu IQMD isospin stopping Momentum ratio in central HIC In nucleon phase space! Symmetry energy && NN cross section 112Sn+112Sn@100MeV/u NUFRA2011 Turkey Liu, J.-Y. et al., Phys. Rev. Lett., 2001, 86, 975

  13. Potentials in IQMD 2 and 3 body interactions (no equilibrium required) Bethe Weizsaecker –mass formula: +symmetry term Volume term (with eos) +Surface term +Coulomb term (+pairing term not included) Hartnack, C. et al. Eur. Phys. J., 1998, A1, 151-169; Nucl. Phys., 1989, A495, 303c-320c

  14. EOS and NN cross section in IQMD nn is the same as pp. Hartnack, C. et al. Eur. Phys. J., 1998, A1, 151-169; Nucl. Phys., 1989, A495, 303c-320c

  15. nucleon phase space cluster phase space IQMD results: phase space Nucleon phase space VS. Cluster phase space Higher stopping in nucleon phase space (red line) comes from the istropic Fermi motion inside cluster !!!! G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  16. IQMD results: centrality 129Xe+119Sn@50 MeV/u INDRA & ALADIN VS. IQMD Mean~0.56 ,width~0.47 Mean~0.56 , width~0.42 • Cluster phase space in IQMD and experimental data can fit each other very well • Impact parameter mixing is serious Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701 G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  17. Sn b IQMD results: time evolution Soft EOS is favored! G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  18. IQMD results: excitation function 129Xe+120Sn • Minimal at Fermi energy • Maximal at 300MeV/u-400MeV/u • EOS dependent! Soft EOS is favored • System size dependent! • Fluctuation Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701 G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  19. IQMD results: excitation function Data: Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701 • Again soft EOS is favored! • System size dependent! • Smaller system, less stopping, higher fluctuation! G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  20. Stopping at cluster level • The heavier fragment, the smaller stopping more transparency • Fermi energy, strongest entrance effect! • Power law of Z-distribution @ Fermi energy • Beam energy dependent! G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011) NUFRA2011 Turkey

  21. Stopping at cluster level ? • The heavier fragment, the smaller stopping • EOS dependent • Beam energy dependent • Fluctuations are still too large to constrain the definite EOS Reisdorf, W. et al., Nucl. Phys., 2010, A848, 366-427 G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612(11) NUFRA2011 Turkey

  22. Multifragmentation or fission or … fusion and evaporation fusion-fission/multifragmentation vaporization RE σ(RE) RE/σ(RE) NN collision Two-body collision Mean field One-body motion E Fermi Energy NUFRA2011 Turkey

  23. Maximal Fluctuation at Fermi energy • Maximal Fluctuation! • Nuclear stopping as L-G transition signal? • Experimental result? NUFRA2011 Turkey

  24. Conclusions and outlooks • The wide-range excitation function of nuclear stopping from 10 MeV/u to 1.2 GeV/u can be described within IQMD. • Minimum at Fermi energy, and Maximum at 300-400MeV/u was observed, consistent with the data. • Apart from 300MeV/u-400MeV/u, no equilibration state is expected during intermediate energy HIC. • In very central HIC, near Fermi energy, there exists the strongest entrance channel effect. • Nuclear stopping shows EOS dependence (soft EOS is favored). • NN cross section is also likely to be determined. • Chemical equilibration? Isospin? Thanks for your attention! NUFRA2011 Turkey

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