Effects of bound-state approximations on distorted-wave Born approximation and multistep processes in the channel-coupling-array theory

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Abstract
The effects of approximating the equations of the channel-coupling-array theory by retaining only bound internal states of the clusters in two-body channels are studied. This approximation corresponds to those used in standard direct nuclear reaction calculations. By use of Lippmann's identity, the exact channel-coupling-array equations may be written in two alternate forms (different off-shell extensions) which respond differently to the bound-state approximation. When the bound state approximation is made on the equations in "folded" form, its main effect is that the distorted-wave Born approximation occurs in only one of the two-body channels, a modified distorted-wave Born approximation occurs in another, and no first order amplitudes of any kind occur in the remaining channels. If Lippmann's identity is first used to unfold the exact channel-coupling-array equations (thereby yielding a different off-shell extension) and then the bound state approximation is applied, distorted-wave Born approximation amplitudes are found in all channels. The need for accurate, nonperturbative solutions to the approximate equations so as to assess the effects of possible loworder approximations is stressed.