Pion Production in Pion-Nucleon Collisions and the Pion-Pion Interaction

The momentum distributions of the pions of all charge states produced in the interaction of 960-Mev ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons with protons are calculated on the assumption of a primary $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction followed by a $\ensuremath{\pi}\ensuremath{-}N$ interaction with excitation of the (3,3) isobar state of the nucleon. The predicted spectra are in reasonable agreement with experimental data when the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ resonance energy is assumed to be about 700 Mev.