An Exact Theory of Inelastic Atom Surface Scattering the “Debye-Waller” Factor

Abstract

The particle surface interaction is decomposed into two parts. The first one is the static periodic potential and yields the elastic diffraction pattern. The second contains the phonon operators and is responsible for the inelastic effects. In the T matrix equation the elastic potential is projected out. The total T matrix element is then given by its elastic component to which is added an expansion containing the phonon operatorsand the coupling between elastic and inelastic channels. A new but simple procedure is presented which allows one to perform the thermal average to all orders in perturbation. Limiting ourselves to the calculation of the thermal attenuation of the diffracted beams the thermal average of T matrix element, which gives directly the diffracted intensity, is written down explicitely. This general and exact procedure is applied to the scattering of a particle by a flat surface. With the simple potential model used the influence of the relation between the reflection coefficient and crystal temperature is not a pure exponential function. This fact is confirmed by careful examination of the experimental data.