Quantum Field Theory of Inelastic Diffraction. II. Two-Step Inelastic Diffraction

Abstract

The consequences of a two-step model of inelastic diffraction are investigated with emphasis on displaying the importance of the relevant conservation laws of total energy and of the component of momentum parallel to the surface. The inelastic energy, loss, and angular profiles for electrons scattered from W(100) are calculated using a model embodying primary Bragg elastic scattering and schematic forms for the coupling between the beam electrons and the elementary excitations of the solid. In general, two peaks in the inelastic energy profile are associated with each peak in the elastic energy profile. Conservation of the component of momentum perpendicular to the surface for the case of a bulk excitation gives rise to a new phenomenon: sideband diffraction. This effect is quite apparent in the angular profiles. Semiquantitative calculations are performed for inelastic diffractions from Al(100) associated with bulk- and surface-plasmon losses. In these calculations we use the sharpjunction semi-infinite jellium model to describe the plasmon dispersion curve, the plasmon lifetime, and the plasmon coupling to the beam electrons.