Phenomenological Study of Pion Photoproduction with Polarized Photons

Expressions for the angular distributions and polarizations of pion photoproduction with polarized photon beams are derived from phenomenological production matrix. The experiments necessary for the complete determination of the multipole amplitudes are discussed in general, and in particular for the case in which only contributions up to $p$ waves in the final state are important. Complete determination requires circularly polarized beams. But if only $s$ and $p$ waves contribute, experiments with linearly polarized beams completely determine the production matrix. The knowledge of these amplitudes would allow the determination of the unknown $p$-wave scattering phase shifts (${\alpha }_{11}, {\alpha }_{13}, \mathrm{and} {\alpha }_{31}$) up to energies of about 300 Mev.