High-Energy Neutron Scattering and the Mihara-Puff Theory of the Structure Factor for Liquid Helium-Four

The ostensible correctness of the Mihara-Puff theory of the structure factor for liquid helium-four and well-known sum-rule expressions are combined to suggest two limiting forms for the dynamic structure factor. One of them is exact in the limit $k\to \infty$ and has the form proposed by Hohenberg and Platzman. We show that it should provide information about Bose condensation if inelastic neutron scattering can be done for $k>\mathrm{}40\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. The other is a simple phenomenological form which applies to the range $3 {\AA }^{-1\mathrm{}}<k<\mathrm{}8\mathrm{} {\AA }^{-1\mathrm{}}$ and is shown to describe successfully the scattering experiments of Cowley and Woods.