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 $v\gg \frac{e^2}{\hslash }$, 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 $\theta$, 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 $\theta \approx 60$°. This process is analyzed both classically and semiclassically, and it is shown that the angular distribution has a sharp peak about $\theta =60\mathrm{}$°.