Quantization of Non-Radiative Surface Plasma Oscillations

Non-radiative surface plasma oscillations in a semi-infinite metal are quantized by using a hydrodynamic jellium model for electrons in the metal. In consequence of the quantization, the electronSF (surface plasmon) vertex function is obtained for the overall region of the surface plasmon wave vector k. In the electrostatic limit, it coincides with the usual electrostatic vertex function obtained by others before. In the extremely retarded limit (k--+0), however, it has a different k dependence from the one predicted by a simple extrapolation of the electrostatic vertex function to the long wavelength region. Our vertex function diverges as k-+ 0, whereas the usual electrostatic one vanish at k= 0 if it is extrapolated to k = 0. By using our vertex function, the long wavelength behavior of the surface loss intensity of scattered electrons passing through the metal foil is also predicted in the case of the normal incidence.