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A theoretical treatment for the ejection of a secondary electron from a clean metallic surface induced by the impact of a fast primary electron is presented. Assuming a direct scattering between the incident, primary electron and the electron in a metal, we calculate the electron-pair energy distributions at the surfaces of Al and Be. Different models for the screening of the electron-electron interaction are examined, and the footprints of the surface- and the bulk-plasmon modes are determined and analyzed.