The surface plasmon dispersion relation for an electron gas

The dispersion and damping of surface plasmons in a semi-infinite free electron gas has been examined using a specular reflection model for electrons at the bounding surface. It is found that this dispersion relation agrees well with the predictions of the hydro-dynamical model for small wave numbers. The damping rate, which is predicted to be zero on the hydrodynamical model, is found to be ≲ 1 % of the plasmon frequency over a substantial range of wave numbers.