Normal modes and the RPA correlation energy of a metallic film

Using a normal mode analysis analogous to that of Sawada et al. (1957), the authors show that Peuckert's expression for the interaction energy of an electron gas confined to a film can be written as the difference in zero point energy between the normal modes of the interacting and noninteracting systems. They consider separately the surface and bulk correlation energies and show that in each case the collective contribution (arising from the plasma oscillation) is small and has the opposite sign to the particle-hole contribution. In particular, the authors show that the surface correlation energy can be regarded as arising almost entirely from the change in the zero point energy of the particle-hole excitations due to the existence of the surface. Due to their omission of this effect, the work of Craig (1972), and Schmit and Lucas (1972) severely overestimates the plasmon contribution.