Information theory and statistical nuclear reactions II. Many-channel case and Hauser-Feshbach formula

Abstract

The information approach developed in paper I is applied to the case of systems having a large number of channels (n ⪢ 1) and arbitrary optical matrices $\text{S}$. The fluctutation cross section is explicitly evaluated using the maximum information-entropy S-matrix distribution constructed to reproduce $\text{S}$ and constrained solely by flux conservation, time reversal invariance, causality, and ergodicity. The resulting expression is found to be the well-known Hauser-Feshbach formula. The evaluation of the cross section is performed with the aid of an auxiliary S-matrix (obtained by a specific mapping from the physical one) which is distributed according to the invariant volume element. The joint distribution for the elements of the physical S-matrix is evaluated in the limit n ⪢ 1 and found to be Gaussian.