Statistical Theories of Fragmentation and Nuclear Disassembly

A general statistical study of fragmentation and aggregation processes is presented and applied to the fragmentation and thermodynamics of heated nuclear matter. Emphasis is placed on distinguishing combinatorial aspects from the statistical and thermodynamic ones. Combinatorial objects pertinent to fragmentation include integer, vector and set partitions as well as permutations. Algorithms for enumerating and randomly selecting these objects, important for statistical models invoking these objects, are presented. Statistical concepts introduced include approximate methods such as Monte Carlo sampling and Markov processes, and exact methods such as recursion relations and generating function identities. Statistical models introduced and solved exactly include the equipartition weight and the Gibbs weight. The canonical Gibbs model is studied extensively, and is shown to be related to symmetric functions and Polyade Bruijn enumeration theory. These exactly solvable models have been applied to Bose-Einstein condensation, the lambda transition in liquid ^4He, polymer gelation, Ewens' sampling formula in population genetics, group social dynamics, statistical shattering, and the enumeration of involutions, graphs and digraphs, indicating their flexibility and power. The application of these models to nuclear fragmentation results in a computationally simplified model which contains most of the essential physics. This model is shown to maintain its structure under coarse graining with suitable conditions on its parameters. The thermodynamics of nuclei allowed to fragment is studied in this context, and predictions are compared with experimental data. A critical comparison of this model to the competing percolation model indicates certain advantages to this approach.