Neutron Scattering from Phonons in Solid Helium

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Abstract
The usual interpretation of the inelastic-coherent-neutron-scattering cross section from phonons in crystal lattices preserves the existence of a one-phonon peak, varying rapidly with neutron energy loss, on top of a smooth multiphonon background, with negligible interference between the two. We point out that previous theoretical analyses arriving at these conclusions are not necessarily applicable to solid helium, since the dimensionless product of neutron momentum transfer and mean atom zero-point displacement is not, in this case, a small parameter. A new expression for the differential cross section is derived, based on a functional variation technique, which allows the dimensionless product to take on an arbitrary value. In the first order of approximation, the one-phonon peak is broadened and shifted from the equilibrium self-consistent phonon spectrum. Estimates are made of the extent to which interference terms distort the observed neutron cross sections in solid helium. The mathematical techniques are also applicable to the model of Feynman et al. for the polaron mobility.