Westcott $g$ Factors Extended to Arbitrary Neutron Energy Spectra

TL;DR

This work extends Westcott $g$ factors to arbitrary neutron energy spectra by implementing two robust methodologies: irregularity-function approximations and direct cross-section integration with ENDF/B-VIII.1 data. It introduces open-source tools (WestcottFactors and a DeCE fork) that enable $g_w$ calculations for Maxwellian and non-Maxwellian spectra, validated against established references and reactor-beam spectra from BRR and FRM II. The results reveal that irregular nuclei with multiple low-energy resonances require cross-section integration for accuracy, as Maxwellian-based estimates can misrepresent $g_w$ by significant margins depending on the spectrum. The study provides Maxwellian tables and reactor-spectrum results, highlighting the practical impact on PGAA/NAA yields and offering software that practitioners can use to tailor $g_w$ to their actual neutron 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{ü}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

Figures (2)

• Figure 1: Low-energy ($E \leq 5$ eV) neutron-capture cross sections from ENDF/B-VIII.1 Nobre24 for each of the isotopes listed in Table \ref{['Table:Resonance_parameters']}. The ENDF/B-VIII.1 cross sections ($\sigma$) are plotted against hypothetical linear (on the log-scale plot) $1/v$ cross sections to show the irregular behavior of these nuclei due to the presence of capture resonances.
• Figure 2: Normalized neutron density functions $p(v)$ for guided cold- and thermal-neutron beams from the PGAA beamlines at the Budapest Research Reactor Belgya12Belgya14 (a) and the FRM II reactor Kudejova08 (b), compared with Maxwellian thermal-neutron density functions $p_{T}(v)$ at various average temperatures $T$.