  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 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 novel applications to a variety of processes where nonlinear
screening plays an important role.
