Theory of Pion Photoproduction

Abstract

The photoproduction of pions from nucleons is calculated in the Tamm-Dancoff approximation to the relativistic pseudoscalar theory. The matrix elements are explicitly separated, in each partial wave, into production into plane waves and production associated with final-state scattering. These matrix elements are exhibited and compared in the energy region up to 500 Mev. The agreement between theory and experiment is fairly good if one uses the same coupling constant used to calculate scattering in this approximation. The enhancement of the $P\frac{3}{2}$, $T=\frac{3}{2}$ ($M1\mathrm{}$) matrix element is about 2.5. A correction (applicable near threshold) for the nonconservation of isotopic spin due to the ${\pi }^{+}-{\pi }^0$ mass difference is evaluated.