Plasmon model for final-state relaxation effects in connection with core-level excitations in metals

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Abstract
A model is presented for calculating the change in the energy of a deep-lying atomic core hole in a metal due to the screening effect of the conduction electrons. The model is highly simplified in that it treats only the plasmon excitations of the conduction electrons but, nevertheless, it seems to contain much of the essential physics. The screening energy is related to the real part of the core-hole self-energy, which is calculated to lowest order. The coupling vertices describing the interaction of the core hole with the surface and bulk plasmons depend on the distance of the core hole from the surface, and hence the screening energy change of the core hole also depends upon this quantity. If the usual approximation is made of assuming dispersionless infinite-lifetime plasmons out to some cutoff wave vector, an exact, analytical expression can be obtained for the self-energy which agrees with the predictions of classical electrostatics when the core hole is far away from the surface. Estimates of the screening-energy difference between a core hole at the surface and one in the bulk are made for Ti, Cr, and Ni and the results compared with values extracted from experimental core-level binding-energy differences between surface and bulk atoms. The magnitude of the effect depends rather sensitively on the choice of cutoff wave vectors. More elaborate calculations of the surface and bulk plasmon contributions to the screening energy are made for Al, where the plasmon lifetimes and dispersion relations are experimentally known quantities, and the results compared with the predictions of the approximation which assumes a dispersionless infinite-lifetime plasmon. In the context of this model a core hole at the surface is screened more effectively than one in the bulk.