Electronic stopping power of aluminum crystal
  Ab initio calculations of the electronic energy loss of ions moving in aluminum crystal are presented, within linear-response theory, from a realistic description of the one-electron band-structure and a full treatment of the dynamical electronic response of valence electrons. For the evaluation of the density-response function we use the random-phase approximation and, also, a time-dependent extension of local-density functional theory. We evaluate both position-dependent and random stopping powers, for a wide range of projectile velocities. Our results indicate that at low velocities band structure effects slightly enhance the stopping power. At velocities just above the threshold velocity for plasmon excitation, the stopping power of the real solid is found to be smaller than that of jellium electrons, corrections being of about 10%. This reduction can be understood from sum rule arguments. 
I. Campillo, J. M. Pitarke, A. G. Eguiluz