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

We present a unified microscopic statistical theory of preequilibrium and equilibrium processes of the compound nucleus, valid for mass numbers A ? 40, light incident projectiles (A ′4), and for excitation energies a few MeV above neutron threshold or larger. 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 parametry 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. We have checked in special cases that the expansion in powers of y is consistent with the consraints imposed by unitarity. Average fluctuating cross sections are given in terms of transmission coefficients and a probability matrix. The latter obeys a probability balance equation, which is shown to be closely related to the Pauli master equation. In case the system equilibraates before it undergoes decay, the average fluctuation cross sections factorize, and we recover the well-known Hauser-Feshbach formula with its various modifications. Next-order correction terms to this formula are also evaluated. The connection between our results, and direct reaction theories on the one hand, and preequilibrium and equilibrium models on the other, is established. These two latter types of models emerge as special cases of the general theory, each with its own well-defined domain of validity, while direct reaction theories specify some input parameters from which channel correlations can be calculated.