Electrodynamic response of a bounded electron gas in hydrodynamic formalism: Theory and applications

Abstract

Coupled integral equations for the electrodynamic response of a bounded electron gas are written down within a unified hydrodynamical model. The nonretarded limit of the formalism is considered in detail and the induced density fluctuation is expressed in terms of the external potential. Within this formalism a simple proof is produced of the known theorem that the long-wavelength surface-plasmon frequency of such a system is independent of either the surface-electron density profile or the hydrodynamic dispersion effect. The theory is applied to the problem of interaction of a moving external point charge with a jellium metal surface. The surface-electron density profile is treated in one- and two-step models. Hydrodynamic dispersion effects as well as the effects of the surface diffuseness and of the finite electron velocity of the external charge on the dynamical image-charge interaction are discussed. The relevance of some of these theoretical results to certain experimental situations involving the interaction of a metal surface with electrodynamic probes is pointed out.