Abstract
A singular boundary condition model with potential tail is developed for theP33 pion-nucleon resonance. The logarithmic derivativeF is given a pole form suggested by theoretical considerations. Both Yukawa and square-well potential tails are treated. It was found that for boundary radiir0=0.50µ−1 or 0.35µ−1 an attractive Yukawa tail of strength − 2µ and range 0.5µ−1 gives an excellent fit to theP33 scattering data correcting violations of the Wigner condition, dF/dE⩽0, previously seen at low energies in zero-potential tail models. Only repulsive square-well tails give good fits, and then the improvement seems to depend on the peculiar behaviour of relativistic corrections. Belowr0=0.20µ−1 the single-pole model merges into a constant-F model withF=−1.95. Attractive tails agree with theoretical studies of the long-range pion-nucleon force.
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