Quantum Field Theory of Inelastic Diffraction. IV. Applications to Al(100) and Al(111)

Results are presented of numerical calculations of the inelastic-low-energy-electron-diffraction (ILEED) intensities of electrons inelastically scattered into the (00) beam from Al(100) and Al(111) via the emission of bulk and surface plasmons. The calculations are based on the isotropic-scatterer version of the theory described in Paper III of this series. The results exexhibit three important systematic features. First, dynamical effects (i.e., those not evident in a kinematical two-step model) are prominent in plots of diffracted intensity versus incident-beam energy (energy profiles), smaller in plots of these intensities versus the electron's exit angle (angular profiles), and unimportant in plots of scattered intensities versus energy loss (loss profiles). Second, dynamical effects in the energy profiles are readily discernible even for weak electron-ion-core scattering. Finally, the contributions to the diffracted intensities due to the "three-step" diffraction-before-and-after-loss processes are found to be exceedingly small relative to those associated with the "two-step" processes of diffraction before or after loss. These features permit us to draw two important conclusions from our analysis. First, the extraction from experimental ILEED intensities of surface-plasmon dispersion relations may be based on a kinematical two-step model provided the analysis is confined to a consideration of loss and angular profiles. Second, the consequences of the vestiges of momentum conservation normal to the surface in a kinematical-model calculation of the excitation of bulk plasmons cannot be distinguished clearly from those of multiple elastic scattering. Thus kinematical momentum-conservation conditions for motion normal to the surface seem to be entirely irrelevant in the interpretation of ILEED intensities.