Hydrodynamic model of linear response for a jellium surface: Nonretarded limit

Abstract

The response of a jellium surface to an external longitudinal perturbation is obtained using a hydrodynamic model to describe the bounded electron gas. The general irreducible response function, which describes the response of the system to the local self-consistent field, is written down. The reducible density-density and density-potential response functions are obtained by solving the response equations for several simple models of the electron density at the surface. The collective modes of the surface are investigated by examining the poles of the response functions. It is shown that the nonlocal effects associated with hydrodynamic dispersion give rise to new structure in the imaginary part of the response functions for the case of nonabrupt surfaces. This structure is then related to the "higher-multipole" modes which may exist in addition to the regular surface plasmon for a sufficiently diffuse surface. The dynamic structure factor is investigated and related to experiments on the energy loss of fast electrons. The effect on these experiments of the existence of "higher-multipole" surface modes is discussed.