3d-shell contribution to the energy loss of protons during grazing scattering from Cu(111) surfaces

Abstract

Motivated by a recent experimental work [S. Lederer and H. Winter, Phys. Rev. A 73, 054901 (2006)] we study the contribution of the $3d$ shell electrons to the energy loss of $100\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ protons scattered off from the Cu(111) surface. To describe this process we use a multiple collision formalism, where the interaction of the projectile with $3d$ electrons is described by means of a sequence of single encounters with atoms belonging to the first atomic layer. In order to compare the theoretical energy loss with the experimental data, we add the contribution of valence electrons, which is evaluated in linear response theory using a response function that incorporates information on the surface band structure. For completeness, the energy lost by protons is also calculated within a jellium model that includes $3d$ and valence electrons with equal footing. Fair agreement between theory and experiment exists when the $3d$ shell is taken into account in the calculation.