Temperature-Dependent Neutron Moderation Model Including Inelastic Scattering in Reactor Media

In this study, a mathematical model of neutron moderation is developed that accounts for the temperature of the fissile medium and the contribution of inelastic neutron scattering on heavy nuclei (U-238) in reactor cores. Within the gas model framework, an analytical expression for the inelastic neutron scattering law for an isotropic neutron source is derived for the first time, incorporating the temperature of the moderating medium as a parameter. The scattering law is obtained from the general kinematic solution of inelastic neutron-nucleus interactions in the laboratory ("L") system, where both particles possess arbitrary velocity vectors. Based on the newly derived inelastic and previously obtained elastic scattering laws, analytical formulas for the neutron flux density and slowing-down spectrum are presented, both dependent on the medium's temperature. The calculated deceleration spectra exhibit two distinct maxima: a high-energy and a low-energy peak. The low-energy maximum is consistent with the analytical solution of the neutron balance equation, confirming the validity of the proposed model. The developed approach provides a deeper understanding of neutron energy distribution in temperature-dependent reactor media and can be applied to improve the accuracy of neutron-kinetic calculations in thermal and fast reactor systems.