An analytic approach to probability tables for the unresolved resonance region

The Unresolved Resonance Region (URR) connects the fast neutron region with the Resolved Resonance Region (RRR). The URR is problematic since resonances are not resolvable experimentally yet the fluctuations in the neutron cross sections play a discernible and technologically important role: the URR in a typical nucleus is in the 100 keV – 2 MeV window where the typical fission spectrum peaks. The URR also represents the transition between R-matrix theory used to described isolated resonances and Hauser-Feshbach theory which accurately describes the average cross sections. In practice, only average or systematic features of the resonances in the URR are known and are tabulated in evaluations in a nuclear data library such as ENDF/B-VII.1. Codes such as AMPX and NJOY can compute the probability distribution of the cross section in the URR under some assumptions using Monte Carlo realizations of sets of resonances. These probability distributions are stored in the so-called PURR tables. In our work, we begin to develop a scheme for computing the covariance of the cross section probability distribution analytically. Our approach offers the possibility of defining the limits of applicability of Hauser-Feshbach theory and suggests a way to calculate PURR tables directly from systematics for nuclei whose RRR is unknown, provided one makes appropriate assumptions about the shape of the cross section probability distribution.