  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.
