Barkas effect in the stopping power for ions with different ionization degrees

The Barkas effect in the electronic stopping power for dressed projectiles moving in a free electron gas is studied for a wide range of velocities v. The interaction of the projectile with the target is described using screened interaction potentials, which take into account the self screening due to the projectile bound electrons and the external screening produced by the target electron gas. The Barkas factor is obtained from a classical simulation of the scattering of the target electrons in the potential of the projectile and that of its antiparticle, following the transport cross section model. A large set of numerical simulations were made for different projectiles, degrees of ionization and velocities. We find that the Barkas factor increases at high energies with the number of projectile bound electrons, whereas its velocity dependence changes from the v-3 behavior for bare projectiles to a v-2 behavior for neutral ones. Interesting effects of curve crossings in the Barkas factor at different degrees of ionization as a function of the projectile velocity are observed. A simple scaling law for neutral and fully ionized projectiles is also derived.