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.

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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

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: 10 2 A MeV ~ A GeV Compare with IQMD ●Describe nuclear stopping in different phase space ●Stopping at event level and fragment level NUFRA2011 Turkey Motivations and outline

NUFRA2011 Turkey Nuclear EOS From GMR D. H. Youngblood, H. L. Clark, and Y.-W. Lui, Phys. Rev. Lett. 82, 691 (1999) Giant Monopole Resonance K 0 =231±5 MeV ρ ~ρ0ρ ~ρ0 soft EOS!

NUFRA2011 Turkey Nuclear EOS Kaon production J. Aichelin and C. M. Ko, PRL55, 2661 (1985) C. Fuchs et al, PRL86, 197(2001) C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, (2006) A soft EOS is favoured! 1ρ 0 < ρ < 3ρ 0

NUFRA2011 Turkey Nuclear EOS from flows Both in-plane flow and out-of-plane flow favor softer EOS (K~300MeV). Danielewicz, P.; Lacey, R. & Lynch, W. G. Science, 2002, 298, ρ 0 < ρ < 7ρ 0

stopping and flow Left: p b=5 fm (b/b max =0.38) Right: y t and y fm ( b/b max <0.15) Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, Andronic, A et al. Eur. Phys. J., 2006, A30, NUFRA2011 Turkey FOPI experiment  Scaled directed flow The ratio of the transverse over longitudinal variances; vartl  1, full stopping, equilibration 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.

Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, Andronic, A et al. Eur. Phys. J., 2006, A30, Peak at 400MeV/u for vartl & flow 2. px dir vs stopping: strong linear correl. 3. Size dependent stopping and flow NUFRA2011 Turkey FOPI experiment 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 EOS from stopping in central HIC? Isospin Equilibrium? Dynamical Equilibrium? pz pt pz pt Nuclear Stopping Isospin tracing Isospin diffusion/transparency Multifragmentation? EOS from nuclear stopping?

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

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, (2007). BQMD FOPI Fu, F. et al. Phys. Lett., B666, (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, (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.... ? AGS SPS 1. No full Equilibration! 2. Low energy? 3. Why? 4. EOS from stopping? Reisdorf, W. et al., Nucl. Phys., 2010, A848, NUFRA2011 Turkey

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

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

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

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

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 !!!! nucleon phase space cluster phase space NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (2011)

IQMD results: centrality Mean~0.56, width~0.42Mean~0.56,width~0.47 INDRA & ALADIN VS.IQMD 1. Cluster phase space in IQMD and experimental data can fit each other very well 2. Impact parameter mixing is serious 129 Xe+ 119 MeV/u NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (2011) Lehaut et. al, Phys. Rev. Lett., 2010, 104,

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

IQMD results: excitation function 1. Minimal at Fermi energy 2. Maximal at 300MeV/u-400MeV/u 3. EOS dependent! Soft EOS is favored 4. System size dependent! 5. Fluctuation NUFRA2011 Turkey Lehaut et. al, Phys. Rev. Lett., 2010, 104, G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (2011) 129Xe+120Sn

IQMD results: excitation function 1.Again soft EOS is favored! 2.System size dependent! 3.Smaller system, less stopping, higher fluctuation ! NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (2011) Data: Lehaut et. al, Phys. Rev. Lett., 2010, 104,

Stopping at cluster level 1. The heavier fragment, the smaller stopping  more transparency 2. Fermi energy, strongest entrance effect! 3. Power law of Fermi energy 4. Beam energy dependent! NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (2011)

Stopping at cluster level Reisdorf, W. et al., Nucl. Phys., 2010, A848, The heavier fragment, the smaller stopping 2. EOS dependent 3. Beam energy dependent 4. Fluctuations are still too large to constrain the definite EOS NUFRA2011 Turkey ? G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, (11)

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

Maximal Fluctuation at Fermi energy NUFRA2011 Turkey 1.Maximal Fluctuation! 2.Nuclear stopping as L-G transition signal? 3.Experimental result?

Conclusions and outlooks 1. The wide-range excitation function of nuclear stopping from 10 MeV/u to 1.2 GeV/u can be described within IQMD. 2. Minimum at Fermi energy, and Maximum at MeV/u was observed, consistent with the data. 3. Apart from 300MeV/u-400MeV/u, no equilibration state is expected during intermediate energy HIC. 4. In very central HIC, near Fermi energy, there exists the strongest entrance channel effect. 5. Nuclear stopping shows EOS dependence (soft EOS is favored). 6.NN cross section is also likely to be determined. 7.Chemical equilibration? Isospin? NUFRA2011 Turkey Thanks for your attention!