Abstract
The authors evaluate the first-order Born perturbation theory for electron capture from atoms by swift ions, with proper allowance for the asymptotic conditions for this three-body Coulomb problem as derived by Belkic et al. (1979). The authors show that the results differ strongly from those of the conventional Oppenheimer-Brinkman-Kramers approximation. Hence the magnitude of the higher terms in the Born series have to be re-evaluated. Some information on this topic is obtained by a comparison between the authors results and those of higher order approximations.