Microscopic theory of retarded Van der Waals forces between macroscopic dielectric bodies

Abstract

In a previous paper we derived an expression for the retarded Van der Waals interaction energy at zero temperature in an arbitrary system of atoms, where an atom was represented by an isotropic harmonic oscillator with one resonance frequency. Starting from this expression we evaluate in this paper the interaction energy between an atom and a semi-infinite dielectric medium, consisting of the same kind of atoms, and that between two dielectric halfspaces. The expressions for the interaction energy can be given in terms of the dielectric constant of the medium, and in this way formulae, earlier derived by Lifshitz from macroscopic considerations are recovered. Limiting formulae for both systems are obtained in the case of small and large separation of the two bodies; furthermore, the first correction (3-particle contribution) to the additive result (2-particle contribution) is given in these limiting cases for both systems.