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

The Reich-Moore formulation is used extensively in many isotope/nuclide evaluations to represent neutron cross section data for the resolved-resonance region. The Reich-Moore 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 Reich-Moore equations are documented in the open literature, computational pitfalls may be encountered with the implementation of the Reich-Moore 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 Reich-Moore 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 Reich-Moore 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 Reich-Moore 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