Variational approach to the scattering of charged particles by a many-electron system

We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering theory, which allows one to obtain nonperturbative scattering cross sections of moving projectiles from the knowledge of the linear and quadratic density-response functions of the target. Our theory is illustrated with a calculation of the energy loss per unit path length of slow antiprotons moving in a uniform electron gas, which shows good agreement with a fully nonlinear self-consistent Hartree calculation. Since available self-consistent calculations are restricted to low heavy-projectile velocities, we expect our theory to have applications to a variety of processes where nonlinear screening plays an important role.V.U.N. and C.S.K. acknowledge support by the Korea Research Foundation through Grant No. KRF-2003-015-C00214. J.M.P. acknowledges partial support by the UPV/EHU, the Basque Hezkuntza, Unibertsitate eta Ikerketa Saila, and the Spanish MCyT.Peer reviewe