We demonstrate that a modified form of the impulse approximation (IA), proposed by Stringari, follows in a natural way from the analysis of Gunn, Andreani, and Mayers. An exact calculation of S(q,ω), for a harmonic system with a Debye density of states, is compared with the prediction of the IA and the Stringari form (SIA). The SIA gives a better description for temperatures less than 0.3${\mathrm{FTHETA}}_D$, where ${\mathrm{FTHETA}}_D$ is the Debye temperature. We derive a simple quantitative criterion for the validity of the IA in terms of the ratio of the atomic kinetic energy and the recoil energy. We argue that the deviations from the IA at low temperatures are primarily due to the quantum nature of the initial state, rather than final-state effects.

• Received 8 August 1988

DOI:https://doi.org/10.1103/PhysRevB.39.2022