Calculation of the Scattering FunctionS(k, ω)for the Inelastic Scatteringof Neutrons by Anharmonic Crystals

Abstract

A numerical calculation is presented of van Hove's scattering function $S(\mathrm{k}, \ensuremath{\omega})$, which describes the inelastic scattering of neutrons by an anharmonic crystal with the transfer of momentum k and energy $\ensuremath{\omega}$ from neutron to crystal. Two contributions to $S(\mathrm{k}, \ensuremath{\omega})$ are included in the present calculation: the leading term which describes the broadening and shift of the one-phonon peak, and the leading term which describes the interference between the one-phonon peak and the diffuse multiphonon background. The calculations of $S(\mathrm{k}, \ensuremath{\omega})$ as a function of $\ensuremath{\omega}$ for fixed k are carried out in the high-temperature limit for a nearest-neighbor, central-force model of a face-centered cubic crystal which is chosen to approximate lead. The $\ensuremath{\omega}$ dependence of the phonon frequency shift and width, as well as of the coefficient of the interference term, is taken into account in these calculations. In the cases treated in the present paper the interference terms represent only a very small correction to the one-phonon peak, in agreement with a previous crude estimate by Ambegaokar, Conway, and Baym.