Plasmon losses in core-level photoemission spectra studied by the quantum Landau formula including full multiple scattering

We study the angular and energy dependence of surface and bulk plasmon losses accompanying deep core excitations in simple metals. Here full multiple scatterings of photoelectrons are taken into account before and after the plasmon losses within the quantum Landau formula, which can describe overall features of the photoemission bands. For example, multiple plasmon loss features can be calculated by use of the formula. Two simple metals, Al and Na, are studied here. The depth profiles of the plasmon losses are strongly influenced by the elastic scatterings. The model assuming single elastic scatterings overestimates the losses from deep emitters due to the forward focusing effects, whereas the model accounting for full multiple scatterings gives a much rapidly decaying function of the depth due to the defocusing effects and rich structures due to the photoelectron diffraction. The single elastic scattering approximation gives a poor result both for the depth profiles and for the loss spectra. The present multiple scattering calculations successfully explain the azimuthal dependence of the loss spectra, which reflect the local geometry around the emitters.