Incoherent Inelastic Neutron Scattering and Self-Diffusion

Abstract

The cross section for incoherent inelastic scattering of neutrons by a many-body system is shown to be related to the real part of a generalized self-diffusion coefficient. The latter quantity is defined as the transport coefficient in the extension of Fick's law of diffusion to arbitrary space-time variations of the driving force. The derivation is based on the fluctuation-dissipation theorem, in a form given by Kubo, and on a treatment of conventional self-diffusion due to Montroll. Previous results, given by Vineyard and by Singwi, Sjölander, and Rahman, are shown to be special cases of the present result.