Nonlinear interaction of charged particles with a free electron gas   beyond the random-phase approximation
  A nonlinear description of the interaction of charged particles penetrating a solid has become of basic importance in the interpretation of a variety of physical phenomena. Here we develop a many-body theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in an interacting free electron gas. Explicit expressions for these quantities are obtained either within the random-phase approximation (RPA) or with full inclusion of short-range exchange and correlation effects. The Z^3 correction to the energy loss of ions is evaluated beyond RPA, in the limit of low velocities. 
T. del Rio Gaztelurrutia, J. M. Pitarke