Separable-Potential Fits to Nucleon-Nucleon Scattering Data

The Arndt-MacGregor (Livermore) nucleon-nucleon phase shifts and mixing parameters for partial waves through $J=4$ are fitted in the energy range 0-400 MeV by separable potentials. We have demanded that the partial-wave scattering amplitudes resulting from our potentials have singularities only for real negative values of the complex energy variable, in addition to the usual right-hand unitarity cut guaranteed by the Lippman-Schwinger formalism. We have also demanded that the appropriate partial-wave amplitudes contain the deuteron pole and the singlet antibound-state pole at the correct energies. The use of these fits in probing the off-energy-shell behavior of scattering amplitudes is discussed.