van der Waals interaction between a point particle and a metallic surface. I. Theory

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Abstract
The van der Waals potential between a neutral atom (no permanent dipole) and a metallic surface is presented. The treatment, based on the normal modes of the system, allows a deeper understanding of the nature of van der Waals forces and makes it practically possible to calculate for complex geometries. To show this we derive theoretical expressions for the interactions of atoms with cylinders and spheres, besides the well-known plane-geometry formula. These formulas are new in some aspects and constitute the theoretical counterpart of many experimental situations. In the same vein we allow a stochastic surface roughness to be present in the plane geometry and show how the problem can be solved analytically in the electrostatic approximation. Numerical calculations and comparison with experiments are presented in paper II.