Size quantization effects in thin film Casimir interaction

We investigate the role of size quantization in the vacuum force between metallic films of nanometric thickness. The force is calculated by the Lifshitz formula with the film dielectric tensor derived from the one-electron energies and wavefunctions under the assumption of a constant potential inside the film and a uniform distribution of the positive ion charge. The results show that quantization effects tend to reduce the force with respect to the continuum plasma model. The reduction is more significant at low electron densities and for film size of the order of few nanometers and persists for separation distances up to 10÷ 50 nm. Comparison with previous work indicates that the softening of the boundary potential is important in determining the amount of the reduction. The calculations are extended to treat Drude intraband absorption. It is shown that the inclusion of relaxation time enhances the size quantization effects in the force calculations.