On the Hydrodynamical Theory for Surface Plasmons

The applicability of the hydrodynamical model, obtained from the high-frequency expansion of the density-density response function, for calculating the surface plasmon dispersion relation and plasmons of higher polarity is analyzed. Of crucial importance to get any result for the dispersion coefficients is that the unperturbed electron density goes to zero at some point. The coefficients obtained for different diffuse electron profiles can be highly unphysical due to "local" plasmons in the tail of the electron gas. This is also the case for the multipolar surface plasmons. A simple theory which includes damping of the local plasmon is found to give very good agreement for the damping of the surface plasmon when compared to more extensive calculations.