Information theory applied to unresolved resonances

The information-theoretical maximum-entropy principle permits to find probability distributions with given averages such as expectation values or higher moments. If the given averages are optical-model phase shifts one obtains the corresponding multivariate distributions of S- and R-matrix elements as the Poisson kernel in the domain of unitary, symmetric matrices and as a generalised t-distribution, respectively. Resonance- averaged cross sections can be calculated as averages over these distributions, i. e. as functions of average S-matrix elements. This constitutes, in principle, a solution of the long-standing Hauser-Feshbach problem, rigorous and general, with direct interactions easily included. In the one-channel case one gets also the cross section distribution in simple analytic form, from which the resonance-averaged transmission is readily calculated.