A stochastic renormalization approach to multifragmentation

Abstract

A new approach for multifragmentation is suggested. The model is based on the following assumptions: the sizes and the number of particles resulting from an individual fragmentation process are random variables; there is no interaction between the particles having different ancestors; the number of fragmentation steps is random and obeys a certain probability law. The stochastic description used shares some features with the theory of branching processes and the multiplicative random walks. Infinite chains of integral equations for the number and size probability densities as well as for the corresponding density functions are derived. For scale invariant systems the limitation of the number of fragmentation steps leads to a renormalization transformation. In this case an explicit solution for the first order density function is derived. The asymptotic behavior of the system is described by two different statistical fractals. They are related to the number and size distributions of the fragments, respectively. The corresponding fractal exponents are determined by different factors and are generally non-correlated.