Abstract
We investigate what makes the solution to the coupled discretized continuum channel (CDCC) equation convergent despite the well-known non-uniqueness of a solution to a single three-body Lippmann-Schwinger equation. It cannot be attributed to the model space assumption, since continuum-continuum coupling (C-C) interactions due to disconnected diagrams are infinite-ranged and can couple an unlimited number of partial waves. The artifice to guarantee the uniqueness is the L2-discretization procedure since it alters the C-C interactions to short-ranged ones. At the same time, it destroys phase relations among three particles. As a consequence, the breakup components become asymptotically dependent on the hyper-radius r as r-3 rather than r-5/2. This implies that, except in the FSI region of breakup products, these should be no breakup cross sections. To emphasize the difference between the CDCC approach and the Faddeev treatment in three-body scattering, we explain how the correct boundary conditions are satisfied in our coordinate space treatment of the Faddeev equation.
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