Crossing symmetric self-consistent πN t matrix

Previous calculations of the self-consistent effective πN t matrix are extended to include a complete, consistent treatment of the pion crossing symmetry. The self-consistent πN t matrix equation is rewritten as a set of four coupled integral equations in order to facilitate the inclusion of crossing symmetry. The πN amplitudes are obtained by means of a Low expansion as in previous papers. The insertion of the crossed πN scattering amplitudes into the nuclear medium is studied in the context of time ordered perturbation theory in order to determine the correct energy at which the crossed amplitudes should be evaluated in the medium. The self-consistent equations are evaluated in nuclear matter. The resonant contribution to the optical potential is found to be broadened by an additional 15--25Xwhen compared to similar calculations which do not include the crossed amplitudes