  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.
