Second-order Born collisional stopping of ions in a free-electron gas

The energy loss of a heavy bare projectile with charge Z_P moving in a free-electron gas is studied within the framework of the binary collisional formalism. The transition-matrix element is expanded in a perturbative series, and terms up to Z_P³ (second Born approximation) are conserved. The Mermin-Lindhard dielectric response function is employed to describe the cylindric potential induced by the projectile. The formalism is applied to the calculation of energy-loss distributions for fixed charges (protons, neutral hydrogen, and antiprotons) colliding with aluminum. We also investigate how the Z_P³ collisional correction affects the total stopping for antiprotons in aluminum and silicon, and for protons in aluminum. In this latest case, different charge states of the projectile are considered. Results are in good agreement with experimental data in the high-energy region.