High-Energy Neutron Scattering from Liquid Helium in the Impulse Approximation

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Abstract
The impulse approximation is used to describe the inelastic cross section for high-energy neutron scattering from superfluid helium in terms of a ground-state momentum distribution of the helium atoms as given by existing variational calculations. The predicted shape of the cross section is compared with recent experimental data and with a previous theory which approximated the noncondensate contribution to the dynamic structure factor by a single-Gaussian function. In contrast to conclusions obtained using the single-Gaussian approximation, our predicted inelastic cross section omitting a condensate contribution provides an acceptable fit to the experimental data. This fit is worsened by introducing a contribution from a condensate fraction in the amount consistent with the variational calculations, namely 11%. If the condensate fraction is arbitrarily reduced from this value, it is found that a much smaller value, with an upper limit of about 3%, is consistent with the available experimental data. It appears that unique assignments of condensate-fraction contributions to inelastic neutron scattering, for the range of neutron energies presently available, will require an improved theory of final-state effects on the shape of the condensate contribution.