Off-shell model of the pion-nucleon T matrix

In the study of pion interactions with the nucleus one requires an off-shell model of the pion-nucleon scattering amplitude. It is desireable to have an amplitude that is not only correct on shell, but also has reasonable off-shell properties. In this work we introduce an off-shell model of the π-N T matrix that is composed of two parts. The first part has the correct s and u channel nucleon poles and the second part is represented by a separable form. The model provides a good fit to the on-shell data up to √s approx. = 1300 MeV and provides a satisfactory representation of the off-shell behavior in the region M/sub N/2 < s < (M/sub N/ + 3m/sub π/)2. This range includes a subthreshold region which is important for the description of low-energy pion-nucleus scattering