Connected kernel methods in nuclear reactions. II. Rearrangement reactions and the distorted-wave series

The newly developed connected kernel equations for $N$-body scattering are applied to the study of rearrangement reactions. An integral equation for the transition operator is obtained which has a connected kernel and whose inhomogeneous terms contain the standard distorted-wave Born approximation (DWBA) and a two-step part. The two-step part is similar to the expression usually used for the calculation of two-step reactions but with a non-standard prescription for the driving potentials. The difference comes about because of the off-shell transformations used to simplify the original connected kernel equations. A multi-step DWBA series is generated and the conditions for its convergence are discussed.