Scaling and final-state interactions in deep-inelastic neutron scattering

Abstract

The momentum distributions of atoms in condensed matter can be determined by neutron inelastic scattering experiments if the momentum transfer $\ensuremath{\hbar}q$ is large enough for the scattering to be described by the impulse approximation. This is strictly true only in the limit $q\ensuremath{\rightarrow}\ensuremath{\infty}$ and, in practice, the experimentally determined momentum distributions are distored by final-state interactions by an amount that is typically 2% to 8%. In this paper we develop a self-consistent method for correcting for the effect of these final-state-interaction effects. We also discuss the Bjorken-scaling and $y$-scaling properties of the thermal-neutron scattering cross section and demonstrate, in particular, the usefulness of $y$ scaling as an experimental test for the presence of residual final-state interactions.