The anharmonic Debye-Waller factor in the classical limit

Abstract

The anharmonic Debye-Waller factor in the one-particle potential model of vibrations is developed for the classical regime for an atom on a site of arbitrary symmetry through a perturbation expansion about the harmonic Hamiltonian. The expression obtained by way of a cumulant expansion is correct to second order, and also sums a whole class of higher-order terms in the conventional treatment. It is pointed out that expressions for the Debye-Waller factor in the recent literature are frequently not even correct to second order. The present formulation allows the Debye-Waller factor to be derived more directly and helps to show which parts of it are Fourier invariant.