Phenomenological Analysis of Single-Pion Photoproduction

A phenomenological fit of the data on single-pion photoproduction is presented for laboratory photon energies up to 1.2 BeV. The analysis is made in terms of a simple model in which the photoproduction amplitude consists of three separate contributions: (1) the Born approximation with electric coupling only; (2) Breit-Wigner resonances for which the positions and widths are taken from pion-nucleon scattering data, but whose amplitudes are adjustable parameters; and (3) additional contributions in the low partial waves having $J=\frac{1}{2},\frac{3}{2},\mathrm{and} \frac{5}{2}$. A criterion for success of the model is that these added terms, which are the principal adjustable parameters, should vary smoothly with energy. Most of the resonances found in the phase-shift analysis of pion-nucleon scattering are included in the fit. In particular, there is reasonably good evidence in the photoproduction data for a broad $S$-wave resonance near 1560 MeV. The analysis is carried out in terms of the helicity-amplitude formalism, which is more convenient for this purpose than the conventional representation in terms of multipole amplitudes.