Energy loss of ions at metal surfaces: Band-structure effects

We study band-structure effects on the energy loss of protons scattered off the Cu (111) surface. The distance dependent stopping power for a projectile traveling parallel to the surface is calculated within the linear response theory. The self-consistent electronic response of the system is evaluated within the random-phase approximation. In order to characterize the surface band structure, the electronic single-particle wave functions and energies are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential. This potential reproduces the main features of the Cu (111) surface: the energy band gap for electron motion along the surface normal, as well as the binding energy of the occupied surface state and the first image state. Comparison of our results with those obtained within the jellium model allows us to characterize the band-structure effects in the energy loss of protons interacting with the Cu (111) surface.