On Wentzel's Method in the Meson Theory

Tatuoki MIYAZIMA, Takao TATI and 5in-itiro TOMONAGA. Summary. As an adequate approximation in case of strong coupling between nucleons and mesons we have Wentzel's method in which solutions are obtained as a power series of the reciprocal of the coupling constant. This method has been discussed ill detail by one of the authors(l) (5. T.) who treated charged longitudinal mesons as an example. In this paper We apply this method to the symmetrical mesons. (2) The principle of the method is the same as the case of the charged longitudinal mesons, we have presented only the main results of our calculation. Also the scattering of mesons by nucleons has been treated by this method. § 1. The fundamental equation and its transformations. The Hamiltonian of the system of symmetric longitudinal mesons and a nucleon at the origin of the coordinates is written as follows: Here l' means the isotopic-spin vector of the nucleon, G is the coupling con-.. These calculations were carried out several years ago, and the contents of this paper were read at the Annual Meeting of the Japan Physico-mathematical Society at Tohoku Imperial University, on July 1'7, 1943, but the wartime trouliles prevented us from pubIi-suing it. In the meanwhile, the strong-couplmg theory was extended by Pauli and his colaborators, and the same problems as ours were treatcd by Serbcr and Dancoff. (Pays. Rev., 63 (1934), 14:t Though they worked out the calculations using the ordinary coordinate space, antI ours are based on the mOllle'1tUnl space, the essential contents are, of course, the same. But our calculations were alsp rigorously carried out to the vihrational states, and the scattering cross-section was obtained by our method.