Microscopic Theory of Pion Production and Sidewards Flow in Heavy-Ion Collisions

Abstract

Nuclear collisions from 0.3 to 2 GeVInucleon are studied in a microscopic theory based on Vlasov's self-consistent mean field and Uehling-Uhlenbeck's two-body collision term which respects the Pauli principle. T h e theory explains simultaneously the observed collective flow and the pion multiplicity and gives their dependence o n the nuclear equation of state.PACS numbers: 25.70.-z One of the most intriguing motivations for studying relativistic nucleus-nucleus collisions is the unique opportunity to explore compressed and excited nuclear matter in the laboratory. A signature of compression is the collective sidewards flow predicted theoretically by nuclear fluid dynamics' and classical microscopic many-body s i m u~a t i o n s .~ Recently, the predicted collective sidewards flow has been observed in highmultiplicity selected collisions of heavy n~c l e i .~,~ Another observable compression effect predicted by fluid dynamics is the dependence of the pion multiplicity o n the nuclear compression energy at high densit i e~.~ The pion multiplicities have been measured for near-central collisions of Ar (0.3-1.8 GeV/nucleon)Both data sets present a challenge to microscopic theories: The flow calculationsL4 done with the standard intranuclear-cascade p r~~r a m s ' .~ result in forward-peaked angular distributions, in contrast to the data. and the calculated pion m~l t i~l i c i t i e s~-~ drastical-I ly overestimate the experimental yields. These large discrepancies are surprising in view of the success of the cascade model in describing inclusive data.'j8 It has been conjectured6 that the difference between measured pion yields and cascade predictions is due to the neglect of compression energy in the cascade approach and thus may be used to extract the nuclear equation of state at high densities.In this Letter we present a microscopic theory which explains for the first time simultaneously both the observed collective flow and the pion multiplicity and gives their dependence o n the nuclear equation of state. Our approach is based on Vlasov's equation for the evolution of the single-particle distribution function f of a collisionless plasma in a self-consistent mean potential field supplemented by UehlingUhlenbeck's quantum mechanical extension of Boltzmann's two-body collision term which respects the Pauli principle. This extended Boltzmann equation can be ~r i t t e n~. '~ The Vlasov equation is solved by simultaneous numerical integration of the classical equations of motion of fifteen parallel ensembles of A p + A T test particles, which are initially assigned Fermi momenta and random positions in a sphere of nuclear radiiis. The ensemble-averaged phase-space density is computed at each synchronization time step in a six-dimensional sphere around each test particle. This ensemble a~e r a g i n g~, '~ ensures a reasonably smooth singleparticle distribution function f (r,p,r) which is used to determine the mean field U ( n) and the Pauli-blocking probability ( 1 -,f) ( 1 -, f ) .

Azimuthal correlations of pions in relativistic heavy-ion collisions at 1 GeV/nucleon

“…The three-body term in V [18,31]. A fit of the momentum dependence to measurements [43,44] of the real part of the nucleon optical potential [6,21,45] yields:…”

“…The first widely used microscopic models for the description of relativistic heavy ion collisions were based on the Vlasov-Uehling-Uhlenbeck (VUU) theory [18,31,32], which explicitly treats nonequilibrium and (stochastic) quantum effects in the framework of one-particle quantities, as well as the nuclear potential (nuclear equation of state). The dynamical basis of the VUU-model is the following transport equation:…”

“…This was motivating a strong experimental effort (4π analysis of streamer chamber events at the BEVALAC) [13][14][15]. However, the sensitivity of pion yields and spectra [16] on the equation of state is not very high [17,18] and therefore the attention shifted towards subthreshold production of mesons (e.g. kaons and η-mesons) [19][20][21][22][23].…”

N-body collisions in high-energy nuclear reactions

“…Here p is the momentum of the intermediate particle and J((p) is the Fourier transform of the propagators (3) and (5). After averaging over the initial spin and isospin, and summing over the.…”

Fermionic Molecular Dynamics

“…In addition the mean free path of the nucleons becomes shorter than the diameter of the system due to the larger intrinsic excitation energy. In BUU-type models [11,12,13,14,15,16] a random Boltzmann collision term has been introduced to account for the shorter mean free path, but the long range part of the two-body interaction is still treated in a mean field fashion. The next step has been to replace the mean-field part by classical molecular dynamics with soft phenomenological two-body potentials [17,18].…”