Surface effects on the electronic energy loss of charged particles   entering a metal surface
  Surface effects on the electronic energy loss of charged particles entering a metal surface are investigated within linear-response theory, in the framework of time-dependent density functional theory. Interesting phenomena occur in the loss spectra originated by the boundary (bregenzung) effect, which is as a consequence of the orthogonality of surface and bulk excitation modes. Our calculations indicate that the presence of a non-abrupt electron-density profile at the surface severely affects the nature of surface excitations, as deduced from comparison with simplified models. 
A. Garcia-Lekue and J. M. Pitarke