Charge exchange and threshold effect in the energy loss of slow projectiles

In this Letter, we study charge exchange and energy loss of protons, taking into account the dynamics of both nuclei and electrons during the collision with atomic hydrogen, helium, and neon targets. We obtain the nuclear and electronic contributions to the energy loss as well as the charge exchange probability, and the total cross section for charge exchange. We find a low-energy threshold in the electronic energy loss due to the quantization of excited states. We find that the electronic stopping cross section is not proportional to the velocity of the projectile at very low velocities (energies), as is predicted by electron gas theory. This confirms recent experimental results.