A Connection between Pion Photoproduction and Scattering Phase Shifts

It is found in a rough approximation that meson photoproduction matrix elements can be expressed in terms of meson-nucleon scattering phase shifts and some energy-independent parameters, for photons in the laboratory of 200 to 500 Mev. The parameters are fitted to experiment in the lower portion of this energy region. It is then found that the higher-energy photoproduction data is consistent only with a $p_{\frac{3}{2}}$, isotopic spin $\frac{3}{2}$, phase shift which passes through 90° at a scattering energy of about 180 Mev. It is indicated that the $s$-wave phase shifts remain small.