Rigorous Solutions for Three-Body Rearrangement Reactions and Validity of the Distorted-Wave Born Approximation

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Abstract
In a distorted-wave type of formalism, two well-behaved integral equations have been obtained for a general three-body rearrangement reaction. The inhomogeneous terms of these equations may be considered to provide mathematically meaningful first approximations (MMFA) to the reaction amplitude. In each of the above mentioned cases, the distorted-wave Born approximation (DWBA) forms an integral part of MMFA. The extra terms in MMFA involve multiple-scattering processes and hence, at least in some casés, their matrix elements may be much smaller than those of DWBA term. This suggests that the success of DWBA may lie in the fact that DWBA is the dominating part of an MMFA. Some of the circumstances under which it can happen are discussed.