Angular Momentum Poles of the Nonrelativistic S Matrix for Spin ½ Particles

The study of the structure of the two-particle S matrix as a function of the angular momentum in potential theory is extended to spin-dependent interactions between two spin {} particles, including the tensor force. The results reveal considerable similarity with the spin zero case, including the symmetry properties. The main differences are two branch points at $j=0$ and j=-1 and a pole at j=-1/2. It is shown that judicious combinations of S-matrix elements contain none of these singularities, and, as a result, neither do the scattering amplitudes. Certain modifications of the canonical situation are found in the presence of spin-orbit forces or other orbital angular momentum-dependent potentials. The factorization of the residue of the S matrix is also discussed.