Size-Dependent Plasmons in Small Metal Clusters

Abstract

The collective motion of the system of loosely bound valence electrons is studied within the framework of the TDLDA (time dependent local density approximation) applied to spherical jellium clusters for the magic clusters, or to spheroidal jellium clusters for the non-magic ones. For Na n Clusters the main results are the following: 1. A well-defined surface plasmon does exist in the size-range 100 < N < 200. Here the surface plasmon line exhausts the Thomas-Reiche-Kuhn sum rule of the oscillator strength to nearly 100%. 2. In the size range N < 40 the surface plasmon is ruined by Landau fragmentation, i.e. the line splits in many lines which have their origin in individual particle-hole-pair excitations. 3. Landau damping does not exist, simply because the surface Plasmon frequency is always lower than the first ionization potential of the cluster. 4. In the optical spectra the intensity of the volume plasmon excitation is smaller by 3 orders of magnitude. In order to excite volume plasmons one should performe inelastic electron scattering. 5. In order to take into account the effect of the Coulomb tail we have modified the TDLDA to the SICTDLDA, which amounts to the inclusion of corrections of the self-interaction effects within the framework of PERD-DEW and ZUNGER.