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

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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. A simple formalism of surface modes is briefly presented which makes it possible to obtain a generalization of the Lifshitz results for the case of two semispaces covered by thin layers. Additional clarification 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 tabulated optical data for the complex refractive index of these metals. The computations turn out to be in agreement with perturbation theory up to fourth order in the 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 thin Au layers is computed, and the possibility of neglecting spatial dispersion effects is discussed as a function of the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure nonretarded van der Waals force law between Al and An bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2-4) nm. More exact values of the Hamaker constant for Al and An are determined.
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