Structure dependence of final-state effects in deep inelastic neutron scattering: Quasiclassical theory

Using a quasiclassical approximation, we calculate the Q→∞ limit of S(Q,ω) for finite potentials with a hard core. For y≡m(ω-ħ$Q^2$/2m)/ħQ, we find QS(Q,ω) equals a convolution of the impulse-approximation result $F_{\mathrm{IA}\left(\mathrm{y}\right)}$ with a ‘‘final-state’’ resolution function, $R_{\mathrm{FS}\left(\mathrm{y}\right)}$, which depends on the structure of the material through the radial distribution function g(r). For realistic g(r), $R_{\mathrm{FS}\left(\mathrm{y}\right)}$ has smaller full width at half maximum than the Hohenberg-Platzman prediction, zero second moment, and no Lorentzian wings. We compare with previous theoretical work, and we discuss the determination of momentum distributions in quantum solids and fluids from deep-inelastic neutron scattering data.