Neutron moderation spectrum considering inelastic scattering

TL;DR

This paper derives an analytic expression for the inelastic neutron scattering law considering medium temperature, enabling better understanding of neutron spectra in reactors by including inelastic processes.

Contribution

It provides the first analytic inelastic neutron scattering law considering medium temperature and arbitrary velocities, expanding the theoretical framework for neutron moderation analysis.

Findings

Analytic expressions for neutron flux density and moderation spectrum including inelastic scattering.

Comparison of elastic and inelastic scattering laws with temperature dependence.

Enhanced interpretation of neutron spectrum shaping in reactor media.

Abstract

For the first time an analytic expression was obtained for the inelastic neutron scattering law with an isotropic neutron source within the gas model, considering moderating medium temperature as a parameter. The inelastic scattering law is obtained, based on the solution of the kinematic problem of neutron inelastic scattering on a nucleus in laboratory coordinate system (L-system) in general case. I.e. in case not only a neutron but also a nucleus have arbitrary velocity vector in L-system. Analytic expressions are found for the neutron flux density and moderation spectrum in reactor fissile medium, both in case of the elastic scattering law, obtained earlier by the authors, and in case of the inelastic scattering law obtained in this paper. Both elastic and inelastic scattering laws are considered to be dependent on the medium temperature. The obtained expressions for neutron moderation spectra enable reinterpretation of physical nature of the processes that determine the shape of neutron spectrum in a wide energy range.