Theory of neutron slowing down in reactor media, taking into account inelastic neutron scattering reactions

Abstract In this paper, the basic model of the theory of neutron deceleration is developed, which takes into account the temperature of the fissile medium emitted by an isotropic neutron source and takes into account the contribution of inelastic neutron scattering reactions on heavy cores of reactor media. In this paper in the framework of the gas model, an analytical expression for the inelastic neutron scattering law for an isotropic neutron source, including the temperature of the moderating medium as a parameter, is derived for the first time. The obtained scattering law is based on the solution of the kinematic problem of inelastic scattering of a neutron on a nucleus in the “L”-system in the general case, i.e., when before scattering not only the neutron but also the nucleus has an arbitrarily given velocity vector in the “L”-system. For the elastic scattering law obtained by the authors earlier and the new inelastic scattering law, analytical expressions for the flux density and neutron deceleration spectrum in the reactor fissile medium, which also depend on the temperature of the medium, have been found. The calculated neutron deceleration spectra obtained using the analytical expression for the neutron deceleration spectrum have two maxima, high-energy and low-energy. Moreover, the low-energy maximum is contained in the analytical solution of the balance equation describing the neutron deceleration process.