Surface plasmon dispersion relation for spherical metal particles

Using the hydrodynamical model, we have obtained the surface plasmon dispersion relation for spherical metallic particles in the following two cases: (1) a sharp surface cut off in electron density and (2) a diffused electron density at the surface. The diffused density is modelled with a step function. The diffuse nature of the electron density at surface of the metal particle is necessary to understand the experimental result for particles with small radii. Shift in the absorption frequency is estimated and found to be small.