Abstract
The ${P}_{11}$ pion-nucleon scattering amplitude is studied in order to determine the dynamical status of the nucleon. A simple one-channel static model is constructed in which a good fit to the low-energy data is obtained with a Castillejo-Dalitz-Dyson (CDD) pole. If there is, in fact, such a pole, with the strength indicated by our model, then one must conclude that other channels play a significant, although not overwhelming, part in forming the nucleon. It is also possible to reconcile all the available information with a model containing no CDD poles in which the nucleon is formed to a good approximation in the pion-nucleon channel alone. A few ways by which one may hope to choose between the two models are discussed. It is shown how the success of certain "reciprocal bootstrap" calculations can be understood, whether or not a CDD pole is required. The large inelasticity and phase shift in the ${P}_{11}$ pion-nucleon channel at energies of 400 to 600 MeV are probably due to coupling with the $\ensuremath{\pi}\ensuremath{\pi}N$ channel, with all three particles in relative $s$ waves. This latter channel seems to be significant for the properties of the 1400-MeV (Roper) resonance, but probably plays a small role in the formation of the nucleon.
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