Electron Correlational Effects on Plasmon Damping and Ultraviolet Absorption in Metals

Abstract

A calculation is presented of the dissipative part of the wave-number-dependent, high-frequency dielectric tensor of a free-electron gas. The calculation, which is exact to lowest order in $k^2$ and $r_s$, includes dynamical correlational (screening) effects which lie outside the random-phase approximation (RPA). The results, which can be expressed entirely in terms of integrations involving the RPA dielectric functions, differ significantly from those of previous work. The $k^2$ coefficient of the plasmon linewidth is predicted to be about an order of magnitude smaller than that measured in high-energy electron scattering experiments. The source of the discrepancy may be due to the failure of the $r_s$ expansion for metals or to phonon or impurity scattering and interband transitions, which have been ignored in previous work. These effects are discussed here, but have not been calculated. The contribution of electron-electron correlations to optical absorption is shown to be smaller than previously calculated by essentially a factor of the Fermi velocity squared divided by $c^2$. Previous calculations ignored terms arising from the perturbation of the screening electrons by the high-frequency fields; these terms greatly reduce the correlational effects.