Angular Momentum Poles of the NonrelativisticSMatrix for Spin ½ Particles

Abstract

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 ½ 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 $j=0\mathrm{}$ and $j=-1\mathrm{}$ and a pole at $j=-\frac{1}{2}$. 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.