Two-nucleon exchange cuts in the Amado model forn−dscattering

A study is carried out of some of the singularities that occur in the second Born amplitude for elastic $n-d$ scattering as described by the Amado model. It is shown that for real energies this amplitude is analytic in the momentum transfer plane except for a right hand cut, and that the discontinuity across the leading edge of the cut depends only on the on-shell, two-nucleon $t$ matrix. This right hand cut leads to a left hand cut in the energy plane for the partial wave amplitudes. A simple formula which involves only the on-shell $t$ matrix is derived for the discontinuity across the leading edge of the $s$-wave left hand cut. The possible implications of these results for the model dependence of three-nucleon calculations are discussed.