A simple model of prompt neutron leakage self-multiplication for use in nuclear materials assay

Abstract

When assaying special nuclear materials using the passive neutron multiplicity counting method, due account must be taken of prompt neutron leakage self-multiplication in interpreting the various counting rates observed. Most often, in practical work, it is treated as an unknown model parameter to be determined from the experimental data. However, in a learning environment and when planning experiments, it is useful to have a straightforward means to estimate the leakage self-multiplication of a measurement item. In the present work, we develop a simple, hybrid, one energy-group, point-like source model for leakage self-multiplication, implemented with interaction probabilities calculated based on spherical and cylindrical bodies. We use published criticality tables to demonstrate the procedure. We show how the prompt neutron leakage self-multiplication may be estimated rudimentarily, including the effects of neutron scattering within the item. This treatment has considerable pedagogic value because it completes, in a similar conceptual framework, the physical point-model picture commonly used to interpret such neutron correlation counting-based measurements. It provides a straightforward quantitative physics-informed structure for making a forward prediction of the leakage self-multiplication factor of a compact non-reentrant measurement item, which otherwise is introduced as an unknown model parameter to be estimated only from experimental data with no guidance on how the value can be estimated a priori. The numerical scheme has been developed with weakly multiplying objects in mind because they are typical of the kind of items measured by thermal-neutron well-counters for nuclear safeguards accountancy and nonproliferation verification purposes. Another potential use is for the assay of measurement items of known geometry and composition where the prompt neutron self-leakage multiplication can be estimated using the simple model developed, thereby allowing the (α,n) production rate to be treated as the unknown in the practical solution (or inversion) of the usual point-model coincidence equations.