A revised three-dimensional electron gas model to describe surface plasmonic phenomena

The long wavelength limit negative slope of the surface plasmon dispersion curve (for simple metals such as alkali) has been experimentally [1] and theoretically [2] studied for a long time. Yet there is no universally accepted theory. On the other hand, the traditional 3D electron gas model such as Lindhard function [3] is successful in explaining many bulk properties, but not much attempt in literature has been made to account for the surface effects. We worked on the traditional 3D electron gas model, modifying the electron self-energy [4] with a correction due solely to surface, and produced the negative slope naturally from simple calculation. In other words, a revised 3D electron gas model can predict and describe surface plasmonic phenomena by itself.
[1] K.-D. Tsuei, E. W. Plummer and P. J. Feibelman, surface-plasmon dispersion in simple metals, Phys. Rev. Lett. 63, 20 (1989)
[2] A. Liebsch, surface-plasmon dispersion and size dependence of Mie resonance, Phys. Rev. B 48, 15 (1993)
[3] N. W. Ashcroft and N. D. Mermin, Solid State Physics, Brooks/Cole Cengage Learning (1976)
[4] G. D. Mahan, Many-Particle Physics, 2nd edition, Plenum Press, New York (1990)