Strong-potential Born-approximation electron-capture cross sections for realistic atomic potentials

The strong-potential Born approximation to the single-electron capture amplitude in asymmetric ion-atom collisions is discussed in the context of a realistic atomic potential. When finalstate binding effects of the captured electron are neglected, a simple connection between the amplitude in the actual atomic-potential case and the one obtained employing a scaled-hydrogenic model is derived which involves the competing effects of an off-shell multiplicative term depending on the residual, target-ion charge and a phase factor containing the difference of the $s$-wave phase shifts for the two potentials.