The velocity dependence of the stopping power of swift protons and deuterons
in low energy collisions is investigated. At low projectile energies the
stopping is mainly due to nuclear stopping and charge exchange of the electron.
The second mechanism dominates after Ep >=200 eV. A dynamical treatment of the
charge exchange mechanism based on two-center electronic wavefunctions yields
very transparent results for the exchange probability. We predict that the
stopping cross sections vary approximately as v to the 1.35 power for
projectile protons on hydrogen targets in the 1 keV energy region.