Energy loss of MeV protons specularly reflected from metal surfaces

A parameter-free model is presented to study the energy loss of fast protons specularly reflected from metal surfaces. The contributions to the energy loss from excitation of valence-band electrons and ionization of localized target-atom electronic states are calculated separately. The former is calculated from the induced surface wake potential using linear response theory and the specular-reflection model, while the latter is calculated in the first Born approximation. The results obtained are in good agreement with available experimental data. However, the experimental qualitative trend of the energy loss as a function of the angle of incidence is obtained when the valence-band electron model is replaced by localized target atom electron states, though with a worse quantitative agreement.