Reciprocal Bootstrap Possibilities for Baryons

In $\pi N$ scattering, using an $\frac{N}{D}$ static model with linear approximation to the $D$ function, the reciprocal bootstrap between the nucleon and the ($\frac{3}{2},\frac{3}{2}$) resonance is shown to hold for any $l$, with an $I=\frac{1}{2}$, $j=l-\frac{1}{2}$ and an $I=\frac{3}{2}$, $j=l+\frac{1}{2}$ isobar supporting each other. It is also shown that this is in fact the only pair of multiplets capable of reciprocally bootstrapping. The following question is then raised: Given the existence of the pion, what is the simplest possible set of baryon multiplets which can support itself? It is found that the aforementioned pair is in fact the simplest set. All these results are then generalized to $\mathrm{SU}\left(3\right)\mathrm{}$, where this pair becomes a $j=l-\frac{1}{2}$ octet and a $j=l+\frac{1}{2}$ decimet.