Nonlinear, band-structure, and surface effects in the interaction of   charged particles with solids
  A survey is presented of various aspects of the interaction of charged particles with solids. In the framework of many-body perturbation theory, we study the nonlinear interaction of charged particles with a free gas of interacting electrons; in particular, nonlinear corrections to the stopping power are analyzed, and special emphasis is made on the separate contributions that are originated in the excitation of either electron-hole pairs, single plasmons, or double plasmons. Ab initio calculations of the electronic energy loss of ions moving in real solids are also presented, and the energy loss of charged particles interacting with simple metal surfaces is addressed. 
J. M. Pitarke, I. G. Gurtubay, and V. U. Nazarov