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The general theory of neutron scattering is presented, valid for the wholedomain of slow neutrons from thermal to ultracold. Particular attention isgiven to multiple scattering which is the dominant process for ultracoldneutrons (UCN). For thermal and cold neutrons, when the multiple scattering inthe target can be neglected, the cross section is reduced to the known value. Anew expression for inelastic scattering cross section for UCN is proposed.Dynamical processes in the target are taken into account and their influence oninelastic scattering of UCN is analyzed.Comment: 28 pages, latex, 2 Postscript figures, submitted to the European  Physical Journal

Multiple scattering theory for slow neutrons (from thermal to ultracold)