Static polarizability associated with multipole surface plasmons in metallic surfaces

An Euler-Lagrange-type equation is solved to different orders for aplane metallic system perturbed by the externa! operator Q used previously in a sum-rule calculation. This approach managed to reproduce to within a few percent the multipole surface-plasmon energies. The jellium model is used for the positive ionic background and local-density functionals for the Hamiltonian. From the zeroth-order Euler-Lagrange equation a self-consistent ground-state density is obtained and used in the first-order equation to obtain the induced density. From the induced density, several aspects of the system response are considered and special attention is focused on the static polarizability

Multipole surface-plasmon modes on simple metals

The average multipole surface-plasmon energy for simple metals, as well as that of ordinary surface and bulk plasmons, is obtained using energy-weighted moments of the electronic response to sufficiently general external perturbations. A local approximation of exchange and correlation effects is used within a jellium model. Band-structure effects are incorporated through an effective electronic mass. Taking advantage of the transparency of the method, we analyze under what circumstances such modes might be observable. It is shown that due to an interplay between Coulomb and kinetic energies, the multipole modes become unobservable for increasing values of the transferred momentum (q) parallel to the surface. The value of q at which the multipole mode becomes unobservable is much smaller than the cutoff value for Landau damping. The effect of the electronic surface diffuseness is also analyzed. We compare our results with previous density-functional calculations and with recent experimental data for Na, K, and Cs