The Boltzmann equation at the borderline. A decade of Monte Carlo simulations of a quantum kinetic equation

Abstract

There are at least two seemingly contradictory approaches to heavy ion collisions at intermediate energy: the nuclear gas and the nuclear liquid pictures. The idea of the nuclear gas, i.e., the Boltzmann transport equation (BEQ) with two body collisions, gives the space-time evolution of the one body distribution function in the case of a dilute fluid. The idea of the nuclear liquid, i.e., fluid dynamics, describes the dynamics in the case of a dense fluid. The conditions of validity of the BEQ and of fluid dynamics are neither satisfied for colliding nuclei at around 100 MeV/nucleon. The solution of a modified Boltzmann transport equation (MBEQ) with both two and three body collisions, the density dependent mean field, and the Pauli principle allows a more appropriate description. The basic theoretical ideas (as laid down by Wong in the previous decade) and computational ideas (as developed by many groups over the past decade) are described. The computer simulation is done using a very stable and robust Monte Carlo numerical method, which compares well with simple analytical models under restricted conditions, and aids in the understanding of the more complicated dynamics of nucleus-nucleus collisions. Inclusive cross sections, subthreshold particle production, above threshold particle production, and collective flow variables are well described by the model. Fluctuations are calculated in the small amplitude limit. Large fluctuations are discussed, as well as their relevance to fragmentation.