Energy loss of slow protons channeled in Au

The electronic energy loss for low-velocity protons channeled in the 〈100〉 direction of single-crystal Au is calculated. The spatial distribution of valence electronic density in Au is calculated by using the tight-binding linear muffin-tin method [O. K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, 2571 (1984); O. K. Anderson, Z. Pawlowska, and O. Jepsen, Phys. Rev. B 34, 5253 (1986)]. The proton trajectories are determined by numerical integration of the classical equation of motion, and the energy loss is evaluated by using a quantum-mechanical transport cross-section approach with a self-consistent model based on Friedel's sum rule. The results allow us to describe the nonlinear behavior of energy loss with ion velocity observed experimentally. {} 1996 The American Physical Society.