  General theory of neutron scattering (elastic and inelastic) is presented. It
is applicable for the whole domain of slow neutrons and includes as limiting
cases existing theories for thermal and cold neutrons and for elastic
scattering of UCN. New expression for inelastic scattering cross section for
UCN is proposed. It differs from the usually used by proper account of
re-scattering processes. Evidence for small heating and cooling of UCN is
given.
