Separable potential model for the off-shellπNamplitude

A simple model is used to reproduce modern $\pi N$ phase shifts in the $S$, $P$, $D$, and $F$ waves for $T_{\pi }<2\mathrm{}$ GeV (except $P_{11}$). In these channels a rank one, two-channel separable potential model is used and the inverse scattering problem is solved directly. In the $P_{11}$ channel the phase shifts are fit with a separable $t$ matrix which contains a pole at the nucleon mass and an explicit sign change in the phase shift. This model is intended for use in theories of the low and medium energy pion-nucleus interaction where it supersedes the obsolete LT and LMM potentials. The explicit pole in the $P_{11}$ channel should facilitate the inclusion of pion annihilation into the many body problem.