Local-field effects at crystalline surfaces: Electron energy loss from ordered arrays of spheres

Local-field effects at crystalline surfaces are analyzed on a classical sys tem consistent of ordered arrays of polarizable spheres. A theory for the e nergy loss of fast electrons traveling parallel to these arrays is presente d. A spectral representation of the surface response function is used to ca lculate this energy loss. The poles and weights in this representation are determined through the eigenvalues and eigenvectors of an interaction matri x which takes into account the quasi-static electromagnetic fields to an ar bitrary multipolar order. We apply the theory to calculate the energy-loss spectra for cubic arrays of aluminum spheres embedded in vacuum and compare the results with those obtained using a dielectric continuum model.