Deep-inelastic neutron scattering measurements on liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been carried out for temperatures from 0.35 to 4.2 K at a density of 0.147 g/${\mathrm{cm}}^3$. These measurements have a relative resolution comparable to previous reactor measurements, but at a momentum transfer of 23 A${\mathrm{̊}}^{\mathrm{-}1}$. This momentum transfer is sufficiently high that the differences between the observed scattering and that predicted by the impulse approximation are small and are well described by a recent theoretical treatment allowing direct information on the single-particle momentum distribution to be obtained from the scattering measurements. The scattering in the normal liquid phase is broad and featureless with a nearly Gaussian shape. The scattering in the superfluid phase is distinctly non-Gaussian with extra intensity at the peak center consistent with the presence of a Bose condensate. However, no distinct peak due to the Bose condensate is observed even when the effects of instrumental broadening are included. When deviations from the impulse approximation are taken into account using a recent theory, the experimental results at 0.35 K are in excellent agreement with ab initio ground-state variational and Green’s-function Monte Carlo calculations in the superfluid at T=0 K. The results at higher temperatures are in excellent agreement with recent path-integral Monte Carlo calculations in both the normal and superfluid phases. Fits of model functions to the scattering are also presented. The average kinetic energy per atom has been determined and is in good agreement with theoretical predictions and with previous experimental results.

• Received 20 November 1989

DOI:https://doi.org/10.1103/PhysRevB.41.11185