Nonlinear screening and stopping powers at finite projectile velocities

Abstract

We have studied the nonlinear screening and stopping power of charged projectiles moving through a uniform electron gas with velocities up to the Fermi velocity of the gas. Our approach is based on density functional theory and is an extension of previous calculations which consider the screening of the projectile in the zero velocity limit. At the higher velocities considered here, the electrons of the metal occupy a shifted Fermi sphere which leads to an asymmetry of the screening charge density and scattering potential along the line of motion of the projectile. To obtain an approximate self-consistent solution of this dynamic screening problem, we use the spherically averaged density to define an averaged scattering potential (spherical potential approximation). As a specific application, we determine the axial screening charge density and stopping power of antiprotons in an electron gas characteristic of aluminium. Screening nonlinearities are found to be important for the full range of velocities considered. In addition, we find that the stopping power exhibits a linear dependence on velocity up to velocities approaching the stopping power maximum.