2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85364The surface plasmon in simple metal clusters is red-shifted from the Mie frequency, the energy shift being significantly larger than the usual spill-out correction. 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 can have the same order of magnitude.17 pages and 2 figuresAtomic and Molecular ClustersNuclear Theorytext