Connection Between theS-Matrix and the Tensor Force

The present paper is a study of the radial Schr\"odinger equations for the case of an interaction between the lth and the (l+2)nd angular momentum, produced by the tensor force in the presence of spin-orbit coupling. It contains a number of theorems, known for central potentials, concerning the low-energy behavior of the S-matrix, bound states, and zero-energy resonance. The construction, in two stages, of all potentials belonging to a given S-matrix and given bound states, is described. The step from the spectral function to the potential involves the generalization of the Gel'fand Levitan equation given in a recent paper; that from the S-matrix to the spectral function, a procedure due to Plemelj also outlined in that paper. The latter procedure leads to a restriction on the S-matrix necessary for a short range potential to exist. If there is such a potential, it is uniquely determined by the S-matrix, the binding energies, and as many real, symmetric, positive semidefinite matrices as there are bound states.