Computational Experience with the Reich-Moore Resolved-Resonance Equations in the AMPX Cross-Section Processing System

The Reich-Moore (RM) formulation is used extensively in many isotope/nuclide evaluations to represent neutron cross-section data for the resolved-resonance region. The RM equations require the evaluation of complex matrices (i.e., matrices with complex quantities) that are a function of the resonance energy and corresponding resonance parameters. Although the RM equations are documented in the open literature, computational pitfalls may be encountered with the implementation of the RM equations in a cross-section processing code. Based on experience, numerical instabilities in the form of nonphysical oscillations can occur in the calculated absorption, capture, or elastic scattering cross sections. To illustrate possible numerical instabilities, the conventional RM equations are presented, and the conditions that lead to numerical problems in the cross-section calculations are identified and demonstrated for ²⁸Si and ⁶⁰Ni. In an effort to circumvent the computational problems, detailed or revised RM expressions have been developed to efficiently and accurately calculate cross sections for neutron-induced reactions in the resolved-resonance region. The revised equations can be used to avoid numerical problems associated with the implementation of the RM formulation in a cross-section processing code. The revised Reich-Moore equations are also used to demonstrate the improved cross-section results (i.e., without numerical instabilities) for ²⁸Si and ⁶⁰Ni.