Singularities in three-body final-state amplitudes

Three-body amplitudes have two-body threshold singularities over and above those coming from the usual treatments of final-state interactions. These are analyzed both formally and numerically. In the numerical model studies, they account for an important variation of the amplitude. The singularity comes from the "next-to-last" rescattering, and hence, may be represented correctly by any approximate amplitude that has that rescattering, even if the approximation scheme diverges. This may account for the correct shape (not magnitude) of multibody spectra determined with a divergent multiple-scattering series.