Mechanisms for theT=12andT=32Recurrences

The conjecture that inelastic states containing an $f$ meson should provide a natural-recurrence mechanism is investigated. We first treat coupled $N\pi$ and $N_{R}f$ channels where, in seeking a recurrence, $N_R$ denotes the previous recurrence. We establish that the attraction is always maximal for angular momentum and parity corresponding to the recurrence state. We concentrate on the ${\frac{7}{2}}^{+}(T=\frac{3}{2})$ and ${\frac{9}{2}}^{+}(T=\frac{1}{2})$ states, and find that the attraction is strong enough to produce resonances, in fact, as we have computed it, excessively so. We then consider coupled $N_R\pi$ and $N_{R}f$ states, and look for these resonances to occur in $N_R\pi$ scattering. The resonance positions determined by taking this point of view are vastly improved. In particular, if we invoke a static version of $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry we obtain a ${\frac{7}{2}}^{+}(T=\frac{3}{2})$ resonant state in good agreement with observation.