The inelastic scattering of thermal neutrons from liquid helium at 1.2 K has been measured for wave-vector transfers in the range 6.0 ~ Q ~ 12.0 A-1 Oscillations in the widths of the scattered-neutron distributions as a function of Q are observed to persist at least up to 12.0 A-~. A simple physical model suggests that these oscillations, which reflect the presence of final-state interactions and interference effects, have their origin in similar oscillations which occur" in the He-He scattering cross section. Detailed measurements at Q = IO.OA -1 show no evidence of a well-defined condensate peak, and calculations suggest that Q values in the range 50-100 A-1 or greater may be required to observe a separate condensate component in the line shape. A method is developed for eliminating a major part of the effects of final-state interactions from the Doppler part of the distributions, and the corrected data at Q = 10.0 A-1 are analyzed to determine the momentum distribution in liquid helium at 1.2 K. The resulting distribution is found to be non-Gaussian with a well-defined high-momentum tail. The result is compared with the momentum distribution obtained recently by Mook from thermal neutron time-of-flight data near Q = 15 A-~ and with theoretical calculations qf McMillan and of Kalos.