Date of this Version
PHYSICAL REVIEW, VOLUME 159, NUMBER 5, 25 JULY 1967
A modification of the Omnes method is used to solve the singular integral equations for the 3-3 partialwave amplitudes of photoproduction. The effects of multipion production are assumed to be negligible. The method requires a knowledge of the phase at all energies. Consequently, it is necessary to treat the corresponding pion-nucleon scattering problem to determine the eBect of the high-energy behavior of the phase on the solution for the scattering amplitude at low energies. The sharply resonant nature of the problen suggests an approximation in the form of solution, rather than in the Born terms, which leads to relatively simple expressions for the ratios of the 3-3 photoproduction amplitudes to the scattering amplitude and for integrals involving the 3-3 amplitudes, In addition, a modified Chew-Low formula can be derived which should satisfactorily represent the 3-3 phase shift throughout the resonance regions. Finally, the cross sections are calculated in the 3-3 approximation and the results compared with experiment.