Static Strong-Coupling Theory withπandηFields

In the framework of the static strong-coupling approximation, a model with a nucleon source and $\pi$ and $\eta$ meson fields is considered. Characteristically different isobar spectra result, depending on whether the ratio of coupling constants of the nucleon to the $\eta$ and $\pi$ mesons is less than or greater than a certain critical value. In the first case the spectrum of excited states is entirely uninfluenced by the $\eta$-meson fields, with the result that the lowest lying excited state is the well-known (3,3) resonance. But if the coupling constants are such that case II is realized, then the isobar spectrum is drastically changed; in particular a $T=\frac{1}{2}$, $J=\frac{3}{2}$ resonance would be expected as the first excited state. The leading term in the strong-coupling approximation of the nuclear force (potential) resulting from the nucleons exchanging $\pi$ and $\eta$ mesons is also derived.