van der Waals and retardation (Casimir) interactions of an electron or an atom with multilayered walls

Publisher Website
Google Scholar
Abstract
We use the quantized surface mode technique to evaluate the interaction V of a ‘‘particle’’ (an electron or atom) with two sets of plane parallel walls of arbitrary thicknesses and arbitrary permittivities; one set is on one side of the particle and the other set is on the other side. It is shown that a set of walls on either side of the particle can be treated as a single wall with an effective reflection coefficient scrR, a function of the frequency and angle of incidence of an incoming plane wave. The two sets of walls have thereby been effectively reduced to one wall on each side. Using a modified version of the standard image technique—the locations of the images are the usual ones, but the strengths are modified—one finds that the closed form for V can be reexpressed as a sum of interactions of the set of images on a given side with the wall on the other side. Taking various limits (thin walls, thick walls, metallic walls, dilute media) reproduces many known interactions and also provides a number of results not previously obtained. The latter results enable us to give quantitative estimates of the error incurred in approximating a wall of finite thickness by a wall of semi-infinite thickness, or approximating a wall with large permittivity by a wall of infinite permittivity. In an attempt to make the paper user friendly, we provide a tabulation of many of the short-range (van der Waals-like) and long-range (retardation) interactions now known, with equation references.

This publication has 15 references indexed in Scilit: