Two-NucleonTMatrix Half Off the Energy Shell: A Direct Approach

The $T$ matrix half off the energy shell can be expressed in terms of the on-shell $T$ matrix and the difference between the full scattering wave function and the phase-shifted free wave function. This representation allows one to investigate variations in the half-shell $T$ matrix by means of a parametrization of the scattering wave function in the interaction region. Most of our knowledge of the physical constraints on that wave function may then be included. In particular we have studied the arbitrariness remaining in the half-shell $T$ matrix given the following constraints: (1) The on-shell $T$ matrix is given; (2) a specific local potential acts beyond a certain radius; and (3) the wave function is suppressed at short distances. We construct models of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ two-nucleon half-shell $T$ matrix. In a simple one-parameter model satisfying these constraints, the range of variation of the near off-shell behavior is displayed.