Evaluation of nlm-n’l’m’ capture amplitude in the target continuum distorted-wave theory

We present a technique to evaluate the capture amplitude from an arbitrary initial state of the target to an arbitrary final state of the projectile within the framework of target continuum distorted-wave theory recently derived and developed by Crothers and Dunseath. Both integrals in their first-order transition amplitude, T⁽¹⁾, are evaluated into closed form, resulting in a finite number of terms. From our general expression of the nlm-n'l'm' amplitude, the evaluation of T⁽¹⁾ for the 1s-1s capture is straightforward. With this technique, it is now convenient to calculate capture cross sections from higher angular momentum states of the target to any projectile states, which are not so easy to calculate in other second-order theories such as the strong-potential Born approximation.