Theory of relativistic charge exchange with Coulomb boundary conditions

A first-order relativistic theory of electron capture satisfying Coulomb boundary conditions in entrance and exit channels is formulated and evaluated. In this way, the asymptotic time dependence caused by the long-range, properly Lorentz-transformed Coulomb interaction is eliminated from initial and final electron wave functions, and a short-range perturbation is obtained in the transition amplitude. Within this theory, the post and prior forms of the transition amplitude are shown to be equivalent. Numerically calculated cross sections are in good agreement with experimental data. They are slightly larger than those derived from the relativistic eikonal approximation.