By means of the Lorentz.covariant perturbation and renormalization methods, the effective cross section for r·n-0 process in pseudoscalar meson theory has been obtained with the matrix elements calculated up to the order ef3. The most conspicuous result, which could not be reached in the lowest order calculation, is that the cross section for neutral meson production turns out to be of the same order as that for charged meson, and that the angular distribution for that process is larger in the

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... orward than in the backward direction. Further we have introduced a Pauli.type interaction with suitably chosen coupling constants in order to estimate the effect of the matrix elements of orders higher than ep, and gained a result similar to the above one, only with a smaller value for the coupling constant. . § 1. Introduction and summary 69 The study of the electromagnetic properties of nucleon-meson system appears to be particularly interesting and, if we want to get insight into the dynamical behavior of this system, the r-1I: process is one of the most important problems. The investigation about r-1I:± process including higher order effects has already been made by Koba, Kotani and Nakai,I) and we sh;ll now study the r-1I:° process along the same line with these authors. The existence of 1I:°-meson has been predicted on various experimental and theoretical grounds, and recent experiments at Berkeley2) have indeed confirmed this expectation directly. The facts which seem to have been established hitherto are as follows: (1) The neutral mesons are produced by r-ray with the cross section comparable with those for the charged mesons. 2 ) (2) The angular distribution for r-1I:° peaks in the forward, with the ratio (7450/{7900-2, while that for r-1I:± is nearly isotropic in the laboratory system. 2 ) The absolute values of cross sections amount to: (7900(1I:°) ~3 X 10-30 cm 2 jsterad., (7900(1I:+)=8 X 10-30 cm 2 /sterad. at about 250 Mev of photon energy. 3) (3) The neutral cross section rises much more steeply with energy than does the charged. 4 ) On the other hand, the calculation based on the lowest order perturbation 5 ) shows that the cross section for P+r-P+ 11:0 process is far smaller .than that for the charged meson production and the angular distribution favors the backward rather than the forward direction. These contradictions with the experimental results seem at first sight to add a new difficulty to the current meson theory. In order to remove these faults, many studies have been done from various standpoints. 6)7)8)9)10) We also intend to investigate this problem Downloaded from https://academic.oup.com/ptp/article-abstract/7/1/69/1925457 by guest on