Scattering of Pions by Nucleons in Intermediate Coupling

An intermediate-coupling method of calculation is applied to the meson-nucleon scattering problem for the case of symmetric pseudoscalar mesons, coupled to a fixed extended source through derivative coupling. It is found that the experimentally observed $P$-wave phase shifts can be explained by taking the coupling constant $f^2=0.712\mathrm{}$ and the cutoff ${\omega }_{max}=6.21\mathrm{}$ meson masses. (This corresponds to a renormalized coupling constant ${f_r}^2=0.105\mathrm{}$.)