Surface-plasmon dispersion relation for the inhomogeneous charge-density medium

Abstract

The surface-plasmon dispersion relation is derived for the plane-bounded electron gas when there is an inhomogeneous charge-density distribution in the plasma. The hydrodynamical model is used.Both y and dq/dx are taken to be continuous at the surface of the slab, where y is the scalar potential. The dispersion relation is compared with the theoretical works of Stern and Ferrell and of Harsh and Agarwal. It is also compared with the observations of Kunz. A dispersion relation for the volume-plasmon oscillations is derived which resembles the well-known relation of Bohm and Pines.