Asymptotic form of the third Born amplitude for forward electron capture by a bare ion incident on a hydrogenlike ion

The nonrelativistic asymptotic behavior of the third Born amplitude is determined for electron capture from a hydrogenlike ion or atom by a bare ion incident with a very high velocity. It is assumed that the incident ion is scattered through only a narrow range of angles, of the order of the electron/proton mass ratio. The result for the asymptotic form of the amplitude differs from two previous results. However, for the asymptotic contibution of the amplitude to the forward cross section (i.e., to the cross section integrated over the narrow forward cone) I obtain the same result as obtained previously.