The statistical theory of nuclear reactions for strongly overlapping resonances as a theory of transport phenomena

A unified microscopic statistical theory of preequilibrium and equilibrium processes of the compound nucleus, valid for mass numbers A >approximately 40, light incident projectiles (A<4), and for excitation energies a few MeV above neutron threshold or larger is presented. The theory is based on a two-body random matrix model for the nuclear Hamiltonian, and on the idea of a chain of statistical doorway [hallway] states, populated from the entrance channel in the direction of increasing complexity through a series of two-body collisions. Averages of fluctuating cross sections, and of other observables, are evaluated by taking ensemble averages, and by a method of calculation which is tailored to the dissipative character of the reaction processes under study. An expansion in terms of a small parameter y is introduced. This parameter is defined as a function of the mean level spacing, the spreading width, the decay width, and the rate of change with energy of these quantities, for each group of statistical doorway states of given complexity. Average cross sections, channel correlations due to direct reactions and/or isolated doorway states (isobaric analogue resonances), the probability distribution function for the elements of the scattering matrix, the correlation length of Ericson fluctuations, and the mean nuclear lifetime are evaluated to leading order in y. (Auth.)