The 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.
@article{arxiv.physics/0306058,
title = {Variational RPA for the Mie resonance in jellium},
author = {G. F. Bertsch and C. Guet and K. Hagino},
journal= {arXiv preprint arXiv:physics/0306058},
year = {2007}
}