Multipole vibrations of small alkali-metal spheres in a semiclassical description

Abstract

We use the jellium model and a semiclassical version of the energy-density variational method to investigate static properties of spherical metal clusters and obtain excellent agreement with the (averaged) microscopical results. Exploiting random-phase-approximation (RPA) sum-rule techniques, we calculate the eigenmode spectrum for collective multipole vibrations of the electrons, including coupling between surface and volume plasmons. In the classical limit the old Mie result is recovered for the surface plasmons of all multipolarities. From the sum rules, we estimate the static dipole polarizabilities and the position and width of the electric dipole resonance. We find that the RPA estimate of the width is in qualitative agreement with recent experiments on small Na clusters.