Divergence of the Distorted-Wave Born Series for Rearrangement Scattering

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Abstract
The convergence of the Born-series solution for the exact, three-body scattering amplitude for rearrangement processes is investigated in the framework of the distorted-wave formalism. An integral equation for the three-body scattering operator is derived, such that the inhomogeneous term is just the "direct" or the distorted-wave Born term. It is shown that the iterative solution to this integral equation diverges, since the kernel of the equation contains three-particle disconnected diagrams, and is therefore not completely continuous. As a consequence, the distorted-wave Born term must be questioned as the lowest order approximation to the exact amplitude.