Microscopic theory of pion production and sidewards flow in heavy-ion collisions.

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 on 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) + K C I . ~ 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 ~ ~ drasticalI 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 on 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 ~ . ' ~