Angular-distribution peak at 60° in electron capture from a heavy atom by a fast light ion

A light ion, incident on a heavy atom with a speed ve², may capture an outer electron as follows: The ion first hits the electron and knocks the electron out of the atom with a speed v. The ion then scatters elastically, through an angle θ, from the target nucleus so as to finally move in the same direction, and with the same speed, as the emergent electron. Kinematics require that θ≈60^∘{}. This process is analyzed both classically and semiclassically, and it is shown that the angular distribution has a sharp peak about θ=60^∘{}.