Distorted wave theory of multi-step processes in direct reactions with applications to successive nucleon transfer mechanisms

A general and an exact distorted wave ''On-Shell Method'' is formulated to describe the multi-step processes in direct nuclear rections. This method makes use of the non-linear form of the distorted wave transition matrix equation corresponding to a dispersion theory approach first developed by Robson. The generalized optical theorem for two-potential-scattering is used to eliminate the multi-step ''off-shell'' contributions entirely. The on-shell method is applied to the successive transfer mechanism in the (p,t) reactions on 206Pb target nucleus. It is shown that the two-step p → d → t mechanism provides a good description of the forbidden (in the zero-range one-step DWBA sense) transition leading to the unnatural parity 3+ state in the 206Pb nucleus. The inclusion of the singlet state of the deuteron with an appropriate Q-value corresponding to the binding energy of --70 KeV in the calculations does not spoil the good fit obtained with the triplet deuteron contributions alone. The calculations of the allowed transitions to the 0+, 2+, 4+ states in 206Pb nucleus show in general that the successive transfer mechanism p → d → t alone is not sufficient to account for the data, showing the need to include other multi-step processes. In the case of the allowed transition to the 0+ state, although the reproduction of the angular distribution shape is fair, the magnitude of the cross-section is smaller by a factor of around 6. The fit to the angular distributions is rather poor in the case of the 2+ and 4+ transitions. (auth)