A dielectric response approach to the dynamic image potential of a charged particle approaching a planar metal surface is formulated. A self-consistent scheme for calculating the instantaneous speed of the particle, and its image potential is also derived. It is shown that the scheme does not rely on the actual approximations made while describing the response of the metal with surface. Various approximations are discussed and the corresponding numerical results compared. The effect of self-consistency and inclusion of dispersion in metal is noticeable.

Van der Waals’ attractive interaction between a neutral atom and a metal surface (semi-infinite jellium) is studied via dielectric response approach in the non-retarded limit. It is shown that the interaction energy can be written in terms of the same form factorF(k, ω), which appears in the formula for dynamic image potential and which depends on the density-density response function of only the metal. The interaction energy written as the change in the zero-point energy of the electromagnetic fluctuations is expressed in terms of a secular determinant whose elements consist of the response function of the metal and the dynamic polarizability of the atom. The usual classical result is obtained when the coupling between the atom and metal is small. In the present analysis, it is shown that for short atom-metal separations, this coupling is important and yields substantial modification over the classical result. Numerical results for such situations are presented for the non-dispersive description of metal and a few inert gas atoms.