Off-energy-shell continuation of the nucleon-nucleon and meson-nucleon transition matrices in the presence of inelasticities

A technique for constructing the nucleon-nucleon transition matrices T in the presence of inelastic channels is given. The present technique avoids the usual potential fit and continues T off the energy shell directly consistent with the two-body scattering data and consistent with the properties of possible two- body bound states. The respective T matrices are determined by a real symmetric matrix function of the continuous energy variable E and the discrete eigenchannel label $alpha$. The on-shell part of sigma is given by the eigenphases; the arbitrariness of T is the off-shell continuation of the phase-shift matrix into two dimensions. The present technique of constructing T makes the experimental nucleon-nucleon and meson-nucleon scattering data readily available as input for nuclear theory extended to include baryon resonances. (AIP)