Classical cross section for charge transfer via "knock-on" capture from high-Rydberg states at asymptotically high impact velocities

Abstract

It was shown recently that the classical treatment of Thomas for the double-scattering contribution to capture by a fast-moving ion of an electron from a hydrogenlike atom in its ground state: a state for which the classical description is surely not precise: becomes exact when applied to capture from a high-Rydberg state: That is, summed over all final bound states, the classical cross section becomes equal to the quantum-mechanical cross section when the initial state is a high-Rydberg state. It is here shown that the classical treatment of Bates and Mapleton for ''knock-on'' capture from the ground state also becomes exact (in the same sense as above) when applied to capture from a high-Rydberg state. The radiative and Brinkman-Kramers mechanisms, which are important for capture from the ground state at high impact velocities, vanish in the classical limit.