Theory of inelastic scattering of cold neutrons from liquid helium

A measurement of the energy losses of monoenergetic neutrons scattered from liquid He II would permit a determination of the energy-versus-momentum relation for the elementary excitations (phonons and rotons) in the liquid. A major part of the scattering at a fixed angle arises from production or annihilation of a single excitation and appears as sharp lines in the energy spectrum. From the position of these lines the energy-versus-momentum relation of the excitations can be inferred. Other processes, such as production or annihilation of multiple excitations, contribute a continuous background, and occur at a negligible rate if the incident neutrons are slow (λ~>4A) and the helium cold (T