The Intermediate Coupling Theory of the Pseudoscalar Meson-Nucleon Interaction

Tomonaga's intermediate coupling theory for scalar mesons is extended to pseudoscalar mesons with pseudoscalar coupling. The single free nucleon is discussed. Recoil is included nonrelativistically and the divergences are removed arbitrarily by a cutoff at the nucleon rest mass. Effects involving one virtual pair are allowed for, on the assumption that two or more virtual pairs may be neglected. The calculations are of a preliminary nature and certain possibilities for refining them are discussed. As they stand, they indicate that even for $\frac{f^2}{4\pi }\simeq 10$, a renormalized weak coupling expansion should give a very slowly converging, but not entirely distorted picture of the meson cloud surrounding a nucleon for pseudoscalar coupling.