Second-order dielectric stopping of ions in a free-electron gas - art. no.022902

The energy lost by a heavy projectile, with charge Z(p), moving in a free-e lectron gas is studied within the framework of the dielectric formalism. In this model, the potential induced by the projectile is expanded in a pertu rbative series, and terms up to second order in Z(p) are conserved. The obt ained quadratic potential is expressed as a function of the first-order die lectric 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 ar e investigated, and in the case of antiprotons, the second-order term is mo dified to avoid negative probabilities. The total stopping power, calculate d taking into account the inner-shell contribution and different charge sta tes in equilibrium, is compared with experimental data. The induced electro nic density is also studied, and results agree with those derived from the density-functional theory.