Random-Field Problem: Perturbations at a Lattice Site Due to Randomly Distributed Impurities

Abstract

The problem of computing the field or other perturbation at a lattice site due to a random collection of impurity centers is considered. The Fourier transform of the field probability density is shown to be of the form exp[−n̄Ψ(t)], where n̄ is the average concentration of impurities and Ψ(t) is an integral that is a function of the individual center–impurity interactions. The Fourier transform is used to calculate numerous quantities that are functions of the random field. Emphasis is placed on computing luminescent decay forms and the energy-transfer probability from one center to surrounding acceptors, but the application of these calculations to the evaluation of other quantities (e.g., partition functions) is also considered. Graphs of some of the computed functions are presented.