On the Nuclear Forces

Abstract

Summary. Generalizing the Lagrangian of the interaction as has been done by Schoen­ berg, and assuming the relations between coupling constants in the symmetrical and charged spin 0 meson fields, nuclear forces which have the same character as the Bethe s potential by the neutral vector meson theory does will be given. There is, however, no difference between the usual scalar-pseudoscalar mixed theory and our generalized interaction one in the approximation adopted here. § 1. Introduction. In studying the interaction of mesons with nucleons the pseudoscalar meson theory has been considered by several authors. For many years the central problem of the meson theory has been to look for a satisfactory type of the meson field to explain the properties of nuclei by the customary perturbation method. As is well-known, definite advances towards the understanding of the divergence problem have been made. Recently, using the newly developed method easel) ~nd others!) showed that the additional nuclear magnetic moments calculated by the pseudoscalar meson theory in the Tomonaga-Schwinger formalism could not fit the existing experimental data in all cases, namely, neutral, charged and symmetrical theories. This point is the serious difficulties for the present meson theory. It must be, however, noted that, although it is hardly possible for us to decide the type of the meson which interacts with nucleons by investigating only the nuclear magnetic moment, still, the difficulty is the important disproof for the present meson theory. On the other band, considering that many results obtained by the pseudoscalar meson field have been in agreement with various experimental data, one could not discard it at once. In the present situation there seems to be another pro­ blem on the pseudo scalar meson theory. That is the Dyson's theorem!> concerning the interactions between mesons and nucleons. Dyson has shown that the pseudoscalar interaction and the pseudovector one are completely equivalent for the first order radiative process. It is suggested from his argument that we * Preliminary report of the results appeared in Prog. Theor. Phys. 4 (1949), 572. 102