Spectrum of surface-mode contributions to the differential energy-loss probability for electrons passing by a spheroid

The differential probability of energy loss for a charged-particle beam moving past a spheroid along the direction of a symmetry axis is obtained. Local, frequency-dependent, dielectric functions are used to describe the response of the spheroid and the medium containing the rectilinear trajectory of the beam. While retardation is neglected, all modes are included in the analytical results. Both oblate and prolate spheroids and their counterpart voids are discussed, and numerical results are given for materials of experimental interest.