Density of states in multifragmentation obtained using the Laplace transform method

In equilibrium statistical mechanics, the density of microstates representing the statistical weight associated with a partition of an isolated system into subsystems (fragments) is the convolution of the state densities of the component subsystems. The Laplace transform approximation provides a simple representation of this density. Despite the fact that no external heat bath can be said to exist (the canonical ensemble is not appropriate) the approximation leads to partition probabilities that involve a product of factors (one for each fragment) expressed in terms of a characteristic inverse temperature. We apply the method to nuclear multifragmentation with particular emphasis on a transition that occurs when the major part of the available energy appears as kinetic (as opposed to internal excitation) energy of fragments. Finally, we discuss the shortcomings and advantages of expressing the weights of partitions with fixed total mass (charge) and multiplicity in a simple multinomial form