Role of the kinematics of probing electrons in electron energy-loss spectroscopy of solid surfaces

Inelastic scattering of electrons incident on a solid surface is determined by the two properties: (i) electronic response of the target system and (ii) the detailed quantum-mechanical motion of the projectile electron inside and in the vicinity of the target. We emphasize the equal importance of the second ingredient, pointing out the fundamental limitations of the conventionally used theoretical description of the electron energy-loss spectroscopy (EELS) in terms of the ``energy-loss functions’'. Our approach encompasses the dipole and impact scattering as specific cases, with the emphasis on the quantum-mechanical treatment of the probe electron. Applied to the high-resolution EELS of Ag surface, our theory largely agrees with recent experiments, while some instructive exceptions are rationalized.