Dynamics of many-particle fragmentation in a cellular automaton model

A three-dimensional cellular automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of fragmentation. The range of impact energies is chosen low enough, to secure that a compound bound cluster can be formed. The model is devised to simulate the laboratory set-up of fragmentation experiments as monitored by 4 pi detectors. The particles interact via a Lennard-Jones potential. At low impact energies the numerical experiments following the dynamics of the individual particles indicate a phase of energy sharing among all the particles of the compound cluster. Fragments of all sizes are then found to evaporate from the latter cluster. The cluster sizes, measured in our setup by simulated 4 pi detectors, conform to a power law of exponent approximately 2.6. In an attempt to duplicate the laboratory caloric curves related, in particular, to nuclear fragmentation processes, we introduce several temperature parameters (kinetic temperature of nucleons, kinetic temperature of fragments, reaction equilibrium temperatures). Theoretical caloric curves are then constructed for those temperature parameters, we regard as physically most relevant. Our results show that different temperature definitions generate different curve patterns, indicating that the fragmentation system remains far from thermodynamic equilibrium. The pattern of the laboratory caloric curve for Au-Au collision experiments as derived from a recent analysis [NuPECC Report, 1997 (unpublished)] is reproduced qualitatively by our reaction temperatures.