With the notable exception of the $S$ waves, reasonably good fits to the $\pi N$ phase-shift analyses had been obtained with a phenomenological one-pole, multichannel $N{D}^{-1\mathrm{}}$ model. We show that a two-channel ($\pi N, \pi \Delta$) model with a second pole in only the diagonal $\pi N$ potential yields a good fit to the detailed behavior of the $S_{31}$ partial wave.

• Received 2 September 1969

DOI:https://doi.org/10.1103/PhysRevD.1.360