Interaction of ultra-cold neutrons with condensed matter

A general theory of neutron scattering (elastic and inelastic) is presented. It is applicable to the whole domain of slow neutrons and includes, as limiting cases, existing theories for thermal and cold neutrons and for the elastic scattering of UCN. A new expression for the inelastic scattering cross section for UCN is proposed. It differs from the one usually used by consistently taking into account re-scattering processes. Evidence for slight heating and cooling of UCN is given.