Nucleon Isobars in Intermediate Coupling

The energies of excited states of nucleons are calculated for the symmetric pseudoscalar meson theory with a fixed, extended source. A version of the Tomonaga method, which is shown to be approximately correct in the limit of strong coupling, is used. The calculation is carried out for moderate coupling by using trial functions with 0, 1, 2, and 3 mesons. Numerical results are presented for a source of the Yukawa shape. For coupling stronger than a critical strength which varies with state and source size, isobars are found for angular momenta ½, $\frac{3}{2}$ and for isotopic spins ½, $\frac{3}{2}$. The ($\frac{3}{2}, \frac{3}{2}$) state always lies lowest in energy. A very large source (∼½ the meson Compton wavelength) yields a ($\frac{3}{2}, \frac{3}{2}$) isobar at ∼350-400 Mev excitation, and a degenerate ($\frac{3}{2}$, ½) and (½, $\frac{3}{2}$) pair at ≥500 Mev. Other isobars lie considerably higher. Smaller sources correspond to higher excitation energies in this range of coupling strength.