Stochastic treatment of nonequilibrium ion stopping in solids

Abstract

We study the energy loss of fast, hydrogenlike ions in thin solid foils, in the regime prior to the establishment of the ion-charge equilibrium. The projectile-charge evolution is described by a nonstationary, continuous-time Markov process, while the target response is described by a time-dependent dielectric-response formalism. We first derive the projectile self-energy in the presence of charge exchange, which is used to determine the bound-electron density in a self-consistent manner, by minimizing the total projectile energy in an adiabatic approximation. An expression for the ion energy-loss distribution is then used to derive the average value of the stopping power as a function of the traversal time in the foil, taking into account the projectile screening by the bound electron. The results of calculations for He ions in Al foils show significant coherence effects on the energy losses in the pre-equilibrium regime, which are interpreted by the overlap between the time delay in the target response and the characteristic time scale for the charge-changing collisions of the projectile with the target atoms.