Third-Born-approximation effects in electron capture

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Abstract
We have calculated corrections to the strong-potential Born approximation using the distorted-wave Born formalism of Taulbjerg and Briggs. In the sense of a plane-wave Born expansion, all terms of the third Born approximation, and all ‘‘single switching’’ fourth Born terms are included, but a peaking approximation is needed to reduce the calculation to tractable form. We believe this to be the first calculation to be so complete in the Born sense. Effects of the higher terms are most visible in the valley between the Thomas peak and the forward peak. The Thomas peak is visible in the correction term even though it includes no second Born contributions. We suggest that this may be interpreted as a third Born effect with two ‘‘hard’’ collisions followed by a ‘‘soft’’ collision.