Canonical studies of the cluster distribution, dynamical evolution, and critical temperature in nuclear multifragmentation processes

Partition functions for a canonical and microcanonical ensemble are developed which are then used to describe various properties of excited hadronic systems. Relating multinomial coefficients to a generating function of these partition functions, it is shown that the average value of various moments of cluster sizes are of a quite simple form in terms of canonical partition functions. Specific applications of the results are to partitioning problems as in the partitioning of nucleons into clusters arising from a nuclear collision and to branching processes as in Furry branching. The underlying dynamical evolution of a system is studied by parametrizing the multinomial variables of the theory. A Fokker-Planck equation can be obtained from these evolutionary equations. By relating the parameters and variables of the theory to thermodynamic variables, the thermal properties of excited hadronic systems are studied.