Pion-Nucleon Scattering in the Boundary Condition Model. II. The Second Resonance

Abstract

Good agreement is obtained with experimental information on the second pion-nucleon resonance by considering an explicit coupling to the $\ensuremath{\rho}$-nucleon channel. The dynamics are represented by the boundary-condition model, satisfying analytic and unitarity requirements. The main effect is due to the coupling to virtual $\ensuremath{\rho}$ mesons, in contrast to the $S$-state coupling effects. All the isotopic splitting of the $J=\frac{3}{2}$ $D$ states can be explained by the coupling to the $\ensuremath{\rho}$-nucleon channel. By altering the coupling in accordance with the one-pion exchange diagram the $T=\frac{3}{2}$ 850-MeV "shoulder" is obtained. The boundary-condition radius agrees with the relevant Feynman diagrams of the strip approximation.