Response of Metal Surfaces to Static and Moving Point Charges and to Polarizable Charge Distributions

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Abstract
A phenomenological dielectric approximation is proposed for studying the response of metal surfaces to external charge distributions and is illustrated by detailed calculations using the Thomas-Fermi model. The procedure is based on the replacement of the dielectric-response kernel in a constitutive relation by its asymptotic expression in the bulk region. It represents an alternative to the classical step-density approximation, where the nonuniform density profile near the surface is replaced by the bulk electron density up to an abrupt termination. While the two procedures are equivalent for a local solid, they are quite different in general because of the different nature of the quantitites being approximated by bulk expressions. Detailed applications include the calculation of the image-potential interaction and of the induced surface dipole for static point charges external to the metal surface, the study of the corresponding quantities for charges embedded in the surface, and, finally, the calculation of the effective polarizability of an adsorbed atom and of the image potential and induced surface dipole for a polarizable ion. Comparison with self-consistent surface-model calculations indicates that for charges external to the surface the results for the above-mentioned dielectric approximation are much more realistic than those for the step-density approximation. However, for the case of embedded charges far away from the surface the step-density approximation yields a more accurate result for the surface dipole. A final section is devoted to the generalization of the step-density treatment to time-dependent response problems, assuming specular reflection of electrons at the surface. Some necessary general formulas are derived in a first part, which is then followed by a detailed study of the image-potential interaction for point charges moving uniformly along various prescribed trajectories. Explicit calculations for a local dielectric function indicate a strong dependence of the instantaneous interaction on the past trajectory of the external charge, as well as strong deviations from the quasistatic image potential in some cases. These modifications arise from real and virtual excitation of surface plasmons for particles moving outside the metal, and from both surface- and bulk-plasmon excitation for particles moving inside the metal.