Second-order dielectric stopping of ions in a free-electron gas

Abstract

The energy lost by a heavy projectile, with charge ZP, moving in a free-electron gas is studied within the framework of the dielectric formalism. In this model, the potential induced by the projectile is expanded in a perturbative series, and terms up to second order in ZP are conserved. The obtained quadratic potential is expressed as a function of the first-order dielectric response or Lindhard dielectric function. We apply the formalism to the calculation of stopping for different fixed charges (protons, neutral hydrogen, and antiprotons) moving in aluminum. Energy-loss distributions are investigated, and in the case of antiprotons, the second- order term is modified to avoid negative probabilities. The total stopping power, calculated taking into account the inner-shell contribution and different charge states in equilibrium, is compared with experimental data. The induced electronic density is also studied, and results agree with those derived from the density-functional theory.