Pion-Nucleon Scattering in the Boundary-Condition Model. I. Inelastic Effects onSWaves

$S$-wave amplitudes for both $T=\frac{1}{2}$ and $T=\frac{3}{2}$ $\pi -N$ scattering in the 0-500 MeV range are constructed by means of the boundary-condition model. Included in the Hermitian $F$ matrix is a production channel in which the two outgoing pions are assumed strongly correlated in the $T=0\mathrm{}$, $J=0^{+}$ state. The behavior of the amplitude so derived is in agreement with the present analyses of the experimental data, and shows in a simple manner the mechanism for obtaining a maximum in the cross section through the introduction of an inelastic channel.