Variational RPA for the dipole surface plasmon in metal clusters Original Research Article

The deviation of the ionic background potential in simple metal clusters from the harmonic shape leads to a red shift of the surface plasmon from the Mie frequency, that is considerably larger than the spill-out correction. In order to estimate this effect, here we develop a variational approach to the RPA collective excitations. Using a simple trial form, we obtain analytic expressions for the energy shift beyond the spill-out contribution. We find that the additional red shift is proportional to the spill-out correction and has the same order of magnitude.