Theory of Mössbauer line broadening due to diffusion of Mössbauer atoms via vacancies

Abstract

We have calculated analytically the effect of diffusion on the M\"ossbauer line, especially considering the correlation effects due to diffusion via vacancies. Starting from a hierarchy of rate equations for single-particle densities, pair correlation functions, and higher-order correlation functions we have deduced for small vacancy concentrations an effective equation for the motion of M\"ossbauer atoms which is similar to the well-known "encounter model". The transport of M\"ossbauer atoms is described by an effective jump-frequency matrix which incorporates the temporal and spatial correlations of the atomic jumps induced by a single vacancy. We calculate the effective jump-frequency matrix analytically by an interation with respect to the number of atomic jumps during an encounter. It turns out that the correlation of the atomic jumps diminishes the diffusion broadening of the M\"ossbauer line. This eliminates some of the discrepancies between M\"ossbauer studies and radio-tracer experiments.