Information theory and statistical nuclear reactions. I. General theory and applications to few-channel problems

Abstract Ensembles of scattering S-matrices have been used in the past to describe the statistical fluctuations exhibited by many nuclear-reaction cross sections as a function of energy. In recent years, there have been attempts to construct these ensembles explicitly in terms of S, by directly proposing a statistical law for S. In the present paper, it is shown that, for an arbitrary number of channels, one can incorporate, in the ensemble of S-matrices, the conditions of flux conservation, time-reversal invariance, causality, ergodicity, and the requirement that the ensemble average 〈S〉 coincide with the optical scattering matrix. Since these conditions do not specify the ensemble uniquely, the ensemble that has maximum information-entropy is dealt with among those that satisfy the above requirements. Some applications to few-channel problems and comparisons to Monte-Carlo calculations are presented.