High-order contributions of the Born Series with correct boundary conditions

The electron capture reaction from hydrogenic targets by heavy bare ions is studied. From well known models, such as the Continuum Distorted Wave and the Boundary Born Series, we develop a new approximation within the distort ed wave formalism. In the entry channel the initial distorted wave function is chosen as in the first order of the Boundary Born Series whereas in the exit channel, the final distorted wavefunction is taken as in the CDW mode l. Single differential and total cross sections are evaluated and compared with other theories as well as with experimental data.