Exploration of an Analytical Model for Treating the Unresolved Resonances

The fundamental basis regarding treatment of unresolved resonances and the construction of probability tables and the relevant issues with their application to reactor physics is critically examined. A theoretical model using integral transform techniques is developed that provides a viable alternative to the stochastic-based “ladder” method widely used to construct probability tables. A brief review of the statistical theory for treating the unresolved resonances is presented, followed by a critical examination of these methods. Then a reference method for computing various probability distributions at 0 K is derived analytically for Breit-Wigner resonances. This reference model provides the analytical insight and conceptual basis for extension to the general case of arbitrary temperature. The generalization to arbitrary temperature is accomplished using the Chebyshev expansion while maintaining the general forms of the distributions. Results of extensive benchmark calculations to verify the viability of the proposed method are presented. Finally, there is discussion of the remaining challenges in application of this new analytical approach, in particular, the issue of its extension beyond the Breit-Wigner approximation.