Quadratic response theory for the interaction of charged particles with   an electron gas
  A survey is presented of the theoretical status of quadratic response theories for the understanding of nonlinear aspects in the interaction of charged particles with matter. In the frame of the many-body perturbation theory we study the interaction of charged particles with the electron gas, within the random-phase approximation (RPA). In particular, nonlinear corrections to the stopping power of an electron gas for ions are analyzed, and special emphasis is made on the contribution to the stopping power coming from the excitation of single and double plasmons. Double plasmon mean free paths of swift electrons passing through an electron gas are also discussed. 
J. M. Pitarke and I. Campillo