Casimir and van der Waals force between two plates or a sphere (lens) above a plate made of real metals

Abstract

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated accounting for the finite conductivity of the metals. The simple formalism of surface modes is briefly presented which allows the possibility to obtain the generalization of Lifshitz results for the case of two semi-spaces covered by the thin layers. Additional clarifications of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using the optical tabulated data for the complex refractive index of these metals. The computations turn out to be in agreement with the perturbation theory up to the fourth order in relative penetration depth of electromagnetic zero point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by the thin Au layers is computed and the possibility to neglect spatial dispersion effects is discussed as a function the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure non-retarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2--4) nm. New, more exact, values of the Hamaker constant for Al and Au are determined.