Negative to Positive Ratio from Nonrelativistic Theories of Pion Photoproduction

A numerical evaluation of the Low theory of charged photoproduction is given in various approximations, including also nonrelativistic recoil of the nucleon. Enhancement of only that part of the ($P\frac{3}{2}, \frac{3}{2}, M1\mathrm{}$) term which is due to interaction with the nucleon current gives reasonably good agreement with experimental data up to 440 Mev. The effect of recoil corrections is hardly discernable in the shape of the angular distribution. The differential cross section is also calculated from a modified version of the theory, called the "adjusted" theory, in which the $S$-wave terms are taken from perturbation theory. This version of the theory gives an equally good fit to the data. The negative to positive ratio is then calculated in the various approximations. It is found that these approximations give nearly the same ratio, although the corresponding predictions of differential cross section for the positive pion production differ greatly. This common prediction for the ratio agrees quite well with the experimental data, especially in the case of the "adjusted" theory.