Free energies across inhomogeneous dispersive media. III. Metals and retardation effects

Abstract

For pt.II see ibid., vol.8, p.3211 (1975). A general expression, including retardation effects, is derived for the van der Walls free energy of interaction between two spatially dispersive semi-infinite half spaces using the infinite barrier model in which the currents are reflected specularly at the interface. The answer is given in terms of model independent longitudinal and transverse bulk dielectric permittivities which are functions of the wavenumber. Numerical estimates of the effects of spatial dispersion on the interaction energy are given using the hydrodynamic model for the permittivities. It is demonstrated that, for two like metallic half spaces across vacuum, spatial dispersion can cause at least a 20% reduction in the effective Hamaker 'constant' at separations approximately=4kF-1 where kF is the Fermi wavenumber. Some inadequacies in the hydrodynamic model are pointed out.