Westcott $g$ Factors Extended to Arbitrary Neutron Energy Spectra

TL;DR

This paper extends Westcott g factors to arbitrary neutron spectra, providing updated calculations and open-source software for neutron activation analysis applications involving non-Maxwellian neutron distributions.

Contribution

It introduces a method to calculate Westcott g factors for arbitrary neutron spectra and applies it to guided neutron beams, updating previous Maxwellian-based values.

Findings

Updated g factors for a broad range of Maxwellian temperatures.

Demonstrated the need for non-Maxwellian g factor calculations for guided neutron beams.

Developed open-source software for calculating g factors with user-specified spectra.

Abstract

Westcott $g$ factors are used in Neutron Activation Analysis (NAA) and Prompt Gamma-ray Activation Analysis (PGAA) to evaluate the impact of non-$1/v$ behavior in the neutron-capture cross sections of certain nuclei on activation product yields. This non-$1/v$ behavior arises from the presence of neutron resonances in the neutron-capture cross sections that overlap with the source neutron spectrum at low ($<5$~eV) energies. Historically, Westcott $g$ factors that have been cataloged for NAA and PGAA applications are the result of calculations that assume a Maxwellian neutron velocity distribution with a given average temperature. In this study, we use this approach with updated neutron-capture cross sections from the Evaluated Nuclear Data File, version VIII.1 (ENDF/B-VIII.1) to tabulate Westcott $g$ factor values for a broad range of Maxwellian distribution temperatures, comparing the results against currently-available $g$ factors from International Atomic Energy Agency tables and other sources. It was discovered during this analysis that the use of guided thermal and cold-neutron beams at certain facilities necessitates an approach for evaluating Westcott $g$ factors based on arbitrary non-Maxwellian spectra. In this paper, we present an approach for calculating $g$ factors with user-specified neutron spectra, and we apply these methods to obtain Westcott $g$-factors for guided- and cold-neutron beams at the Budapest Research Reactor and the Forschungsreaktor M{\"u}nchen II reactor. Open-source software has been developed as part of this study that can be used to perform these calculations for applications in PGAA and NAA experiments