Transport studies of heavy ion collisions and antiproton-induced reactions on nuclei at FAIR energies

Transcription

1 Transport studies of heavy ion collisions and antiproton-induced reactions on nuclei at FAIR energies A.B. Larionov Outline: 1) Motivation. 2) The GiBUU model: kinetic equations with relativistic mean fields. 3) Heavy ion collisions: the role of many-particle collisions and of a mean field. 4) Antiproton-nucleus collisions: the cold compression of a nucleus. WG 3 meeting,

2 Collaborators: O. Buss, T. Gaitanos, K. Gallmeister, and U. Mosel Institut fuer Theoretische Physik, Universität Giessen, D Giessen, Germany W. Greiner 1, I.N. Mishustin 1,2, I.A. Pshenichnov 1,3, and L.M. Satarov 1,2 1 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, D Frankfurt am Main, Germany 2 Russian Research Center Kurchatov Institute, Moscow, Russia 3 Institut for Nuclear Research, Russian Academy of Science, Moscow, Russia

3 Motivation low-energy heavy ion collisions, high density (up to ) nuclear matter created: deconfinement and hadronization: strangeness enhancement, lumping in momentum space due to spinodal instability

4 search for signals of the critical point: particle number ratios (e.g. ) fluctuations in-medium modifications of hadrons: - broadening (dilepton inv. mass spectra), dropping masses, in-medium modified cross sections. many-body collisions at high density

5 antiproton beams at GeV/c. baryon spectroscopy: charm in-medium: double- hypernuclei production: strongly bound antibaryon-nucleus states: nuclear compression by implanted or slowly moving antibaryon

6 GiBUU model Giessen Boltzmann-Uehling-Uhlenbeck model:

7 Relativistic kinetic equation (D. Vasak et al., 1987; H.-Th. Elze et al., 1987; B. Blaettel et al., 1993) : - effective (Dirac) mass - kinetic four-momentum - effective mass shell condition Relativistic mean field (RMF) acting on baryons and antibaryons: non-linear Walecka parameterizations, antibaryon mean field by G-parity transformation with proper rescaling the coupling constants; Collision term includes elastic and inelastic channels and resonance decays. Optionally, 3-body collisions are also included. Test particle method used (mostly in parallel ensemble mode).

8 Gas parameter at (maximal baryon density reached in a central Au+Au collision at 20 A GeV): where mb asymptotic high-energy pp cross section. Many-body collisions are important (St. Mrówczynski, 1985)

9 Three-body collisions: method from G. Batko, J. Randrup, T. Vetter, 1992, modified for relativistic effects define the interaction volume of colliding particles 1 and 2: find the particle 3, which is closest to the c.m. of 1 and 2 inside the interaction volume

10 redistribute the momenta of 1,2 and 3 microcanonically: Dirac mass shell conditions: simulate the two-body collision of 1 and 2 with their new four-momenta and

11 Results for heavy ion collisions A.L., O. Buss, K. Gallmeister, and U. Mosel, PRC 76, (2007)

12 Proton rapidity distributions Cascade gives too much stopping RMF reduces stopping: less collisions due to repulsive ω 0 field Three-body collisions increase thermalization more stopping In-medium reduced cross sections again reduce stopping

13 Cascade and RMF calculations w/o three-body collisions produce too soft m t -spectra of K + and K -. Three-body collisions reduce slope better agreement with data. Pion m t -spectra are not much influenced by three-body collisions.

14 Three-body collisions raise T strongly!

15 Summary for HIC RMF is important to describe the proton rapidity distributions. Three-body collisions, in average, increase transverse momenta of produced particles good (within 10%) agreement with the measured inverse m t slopes.

16 Next steps: Detailed comparison with exp. data on proton, pion and kaon rapidity and transverse mass spectra, elliptic flow, fluctuations at least up to top SPS energies (160 A GeV) Pion and strangeness production at SIS energies Implementation of the momentum-dependent RMF Building the hybrid hydro-kinetic model capable to describe the deconfined stage of a collision.

17 Results for antiproton-induced reactions A.L., I.N. Mishustin, L.M. Satarov, and W. Greiner, PRC 78, (2008) and arxiv: ; A.L., I.A. Pshenichnov, I.N. Mishustin, and W. Greiner, PRC 80, (2009).

18 Cold compression: hadron-doped nuclei radius is shrinked by 20% K. Tanida et al., PRL 86, 1982 (2001) by 30% Y. Akaishi and T. Yamazaki, PRC 65, (2002) What happens with a nucleus with an antibaryon implanted or moving slowly in its interior?

19 Static calculations of - induced compression G-parity potential ρ(fm 3 ) z (fm) 4 16 O r (fm) ρ(fm 3 ) z (fm) 4 16 p - O r (fm) ρ(fm 3 ) z (fm) O Λ r (fm) BE 16 ( O) = 130 MeV BE ( _ O) =1051 MeV 16 p 16 Λ BE ( _ O ) = 565 MeV NL3 NL3 NLZ T. Buervenich, I.N. Mishustin, L.M. Satarov, J.A. Maruhn, H. Stoecker and W. Greiner, PLB 542, 261 (2002).

20 Compression by moving central collisions, w/o annihilation Stronger compression for initially slower and closer to the nuclear centre antiproton.

21 Maximum nucleon density and survival probability of an The probability of annihilation in a compressed state:

22 Inclusive annihilation cross section Relative probability of annihilation at ρ > 2ρ 0

23 Cross section of annihilation at the condition of outgoing proton with momentum > p Relative probability of annihilation at ρ > 2ρ 0

24 Summary for antiproton-nucleus reactions The highest nuclear compression probability is reached at the antiproton beam momenta below 0.5 GeV/c. However, the trigger on a fast proton makes the beam momenta of 3-10 GeV/c preferable for selecting the events with nuclear compression. Next step: (double) hypernuclei production in antiproton-induced reactions

25 Backup

26 Relativistic mean field (RMF) Lagrangian density: A. Lang, W. Cassing, U. Mosel, and K. Weber, NPA 541, 507 (1992) G.A. Lalazissis, J. König, and P. Ring, PRC 55, 540 (1997); I.N. Mishustin, L.M. Satarov, J.A. Maruhn, H. Stöcker, and W. Greiner PRC 71, (2005); A.L., O. Buss, K. Gallmeister, and U. Mosel, PRC 76, (2007).

27 RMF parameter sets: NL2 (A. Lang, W. Cassing, U. Mosel, and K. Weber, 1992) : m σ =550.5 MeV, m ω =783.3 MeV, g σn =8.50, g ωn =7.54, g 2 = fm -1, g3=-6.26 K=210 MeV, at ρ 0 =0.17 fm -3. NL3 (G.A. Lalazissis, J. König, and P. Ring,1997): m σ =508.2 MeV, m ω =782.5 MeV, g σn =10.2, g ωn =12.9, g 2 =-10.4 fm -1, g 3 =-28.9 K=271.8 MeV, at ρ 0 =0.148 fm -3.

28 Antinucleon coupling constants: where 0 < ξ 1 is the scaling factor. (I.N. Mishustin et al, 2005) G-parity transformed nuclear potential: ξ=1. Reduced couplings: ξ=

29 Klein-Gordon-like equations for the σ- and ω-fields: Partial scalar density and baryon current: - spin-isospin degeneracy

30 The test particle method: - number of physical particles of the type, - number of test particles per physical particle. Numerics: gaussian of the width L=0.5 fm. equations of motion for the centroids :

31 Collision integral: E.g., for NN NN elastic scattering: - differential (in-medium) scattering cross section - relative velocity

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38 RMF strongly reduces the hyperon yield at midrapidity. In-medium cross sections reduce meson production.

39 Problem to describe the reduction of above 30 A GeV.

40 Nucleon and antiproton densities and potentials Compressed state is formed during 4-10 fm/c.

41 Central nucleon density vs time Spinodal instability at ρ N < 0.6ρ 0 : - pressure, - entropy per particle Ph. Chomaz, M. Colonna, J. Randrup, Phys. Rep. 389, 263 (2004) multiple fragment formation

42 Nucleon kinetic energy spectra Nucleons are accelerated by processes (M. Cahay, J. Cugnon, P. Jasselette, J. Vandermeulen, PLB 115, 7 (1982)) Compression enhances the slope temperature. Effect is stronger for lighter systems.

43 Annihilation event spectra on the total invariant mass of emitted mesons. Shift of the peak by 0.5 GeV to smaller M inv for light systems due to compression.

44 Baryon density and radial component of the collective flow velocity vs radial distance

45 Collective expansion:

46 Antiproton mean field determination: absorption cross section on nuclei. Data: K. Nakamura et al., PRL 52, 731 (1984) and refs. therein. W/o mean field, GiBUU reproduces a simple Glauber model: Antiproton mean field scaling factor ξ

47 Momentum spectra of protons and pions for p lab =608 MeV/c. Data: P.L. McGaughey et al., PRL 56, 2156 (1986). Pion slope changes at GeV/c due to pion rescattering and absorption: High momentum protons are knocked-out by energetic pions.

48 Rapidity spectra of protons and pions for p lab =608 MeV/c. Data: P.L. McGaughey et al., PRL 56, 2156 (1986).

49 The real part of an antiproton optical potential is -(150±30) MeV, which is far away from G-parity values of -650 MeV, in agreement with a recent analysis of antiprotonic atoms (E. Friedman, A. Gal, and J. Mares, 2005)

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