We have constructed three rank-one energy-independent separable potentials for the pion-nucleon $P_{33}$ channel which reproduce the scattering volume and phase shift up to 350 MeV. The amplitudes were calculated from these potentials using the Blankenbecler-Sugar equation approach and are appropriate for relativistic three-body calculations of the $\pi \mathrm{NN}$ system. An interesting feature of resulting potentials is the appearance of two very different ranges in each. The low-momentum parts of the different potentials are essentially the same but there are significant differences in their high-momentum behavior. Information from $\mathrm{NN}$ pion-production supports the two-range feature of these potentials and favors one of the potentials over the others.

NUCLEAR REACTIONS $N(\pi , \pi )N$; separable potentials for $P_{33}$ channel; calculated $\delta \mathrm{}\left(E\right)\mathrm{}$, $E=0-350\mathrm{}$ MeV.

• Received 28 May 1982

DOI:https://doi.org/10.1103/PhysRevC.26.1761