Structure of the Nucleon. II. Pion-Nucleon Scattering

The scattering of pions by nucleons is treated on the basis of the assumption that the nucleon has a rather complex structure consisting of a core surrounded by varying numbers of pions in certain bound states. The scattering phase shift is found to be composed additively of two parts, an orthogonality phase shift determined by the condition that the incoming wave be orthogonal to the bound field and a phase shift due to the interaction between the incoming wave and the bound field plus core. The former phase is shown to be negative at low energy and to decrease rapidly with increasing energy. The other term is found to have a typical resonance behavior. Each of the parameters appearing in the formulas for the phase shifts is given a rather direct physical interpretation. When the parameters are chosen in such a way as to give a good over-all fit to the data up to 400 Mev the following picture of the nucleon emerges: The bound field consists of $P$ waves concentrated at a small distance (¼ the pion Compton wavelength) from the core and $S$ waves extending to about twice that distance. The states of excitation (resonances) of the bound field consist of the usual $P$ resonance with $J=\frac{3}{2}$, $I=\frac{3}{2}$, and a much broader $S$-wave resonance with $I=\frac{1}{2}$. Indications are that all other states of excitation lie higher (above 300 Mev) and are smeared out into a continuum through the emission of virtual pion pairs.