Abstract
The dispersion approach to the low-energy photoproduction of pions on nucleons is re-examined in such a way as to avoid the contributions coming from the unphysical cosine region. Analytic representations for invariant amplitudes in the squared c.m. threemomentum plane are managed in such a way as to get rid of all but the dynamical singularities. As a first step of the study only the contributions from the direct and crossed photoproduction channels are retained, and relativistic dispersion relations for multipoles are deduced by integration over the scattering angle. Making use now of the unitarity condition in the “two intermediate particles” approximation, and considering the pion-nucleon phase shifts as quantities known from experiment, it is easy to transform the dispersion relations in question into a set of integral equations which are to be solved numerically. The numerical results and their comparison with experiment will be presented in a paper to follow.
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