Theory of deep inelastic neutron scattering. II. Application to normal and superfluidHe4

The hard-core perturbation theory (HCPT) predictions for high-momentum-transfer neutron scattering from liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are numerically evaluated. The input to the calculations are Monte Carlo and variational momentum distributions, the radial distribution function, and the Jeffreys-Wentzel-Kramers-Brillouin phase shifts for the He potential. Consistent with the ${\omega }^2$ sum rule, the Gaussian width of the dynamic structure function S(Q,ω) is the same in HCPT and in the impulse approximation (IA). However, where the IA predicts structure in S(Q,ω) below $T_{\lambda }$ due to the Bose condensate, HCPT predicts that S(Q,ω) is smoothed by final-state broadening. The final-state effects are negligible for the normal fluid above $T_{\lambda }$. The approach to the IA at high Q is shown to be O(logQ) for the He-He potential, which implies that S(Q,ω) satisfies approximate Y scaling and that final-state broadening is significant for all feasible experiments. Extensions of HCPT to lower Q and to other systems are qualitatively discussed. The problem of extracting momentum distributions in quantum fluids and solids from high-Q neutron scattering is addressed.