Generalized Thomas-Fermi-Weizsäcker approach to screening and slowing down of swift charged particles in jellium

A generalized Thomas-Fermi-Weizsäcker theory is proposed to investigate the screening and slowing down of charged particles moving through a homogeneous jellium with arbitrary nonrelativistic velocity. This theory involves a velocity-dependent modification of the Thomas-Fermi kinetic-energy density near the projectile. Nonlinear inhomogeneous integrodifferential equations are derived for the dynamically screened potentials of protons and antiprotons. The stopping power of a noninteracting electron gas for the rotational-symmetric limit of the screened potential is approximated in a simple form. At typical metallic densities, this approximation of the antiproton stopping power finds about half of the equivalent proton stopping power near the electronic stopping power maximum. At lower velocities the results are in fair agreement with previous density functional calculations. In the large-velocity region the two stopping powers merge. Higher approximations including the breakdown of the rotational symmetry are discussed in detail. © 1996 The American Physical Society.