Retarded dispersion interaction between metals

Abstract

The effect of retardation on surface-plasmon dispersion and the Van der Waals interaction between metals is investigated using the hydrodynamic model for the metallic electrons. Our retarded-surface-plasmon dispersion formula for two interacting metal half spaces shows the expected splitting into two branches, but differs markedly from the nonretarded curves at very small wave numbers. In particular, there is a cutoff in wave number below which no modes corresponding to the ${\ensuremath{\omega}}_{+}$ branch can exist. The Casimir result, $\ensuremath{-}\frac{\ensuremath{\hbar}c{\ensuremath{\pi}}^{2}}{240{l}^{4}}$, for the Van der Waals force between the slabs is obtained as the leading term for any two metals in the retarded region, with the parameters, bulk-plasma frequency, and Fermi velocity, defining the particular metals entering in the higher-order correction terms. The hydrodynamic model being equivalent to the use of a nonlocal dielectric function, the divergence in the Van der Waals force is removed as $l\ensuremath{\rightarrow}0$. Numerical results have been obtained for the Van der Waals contribution to the surface energy for 20 metals, and some typical results are plotted.