Theory of van der Waals interactions between metal surfaces

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Abstract
We discuss a theory of van der Waals interactions between metal half-spaces including spatial dispersion effects, which are responsible for the penetration of induced charge fluctuations inside the metals. The starting point is a general expression for the correlation energy of an inhomogeneous system, which is applied in a hydrodynamic description of an electron gas whose mean density is uniform up to the surfaces, where it cuts off abruptly. In the local limit this treatment reduces exactly to the results of the Lifshitz theory based on a phenomenological description of electromagnetic field fluctuations. It is shown that in this limit the van der Waals energy is given by the modification of the zero-point energy of surface plasmons when the separation between the two half-solids is decreased from infinity to its actual value. This provides a direct basis for a procedure introduced by Van Kampen et al. and applied extensively in recent years. In the general case, the van der Waals energy reduces to a similar expression in terms of a zero-point energy difference of plasmons, whose frequencies are modified by electron-hole dispersion effects. The consequences of this dispersion both for van der Waals interaction and for the surface correlation energy of the interacting half-solids are analyzed in detail.

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