SINGLE-PION PRODUCTION IN $pi$$sup -$p INTERACTIONS AT 2.26 GeV/c.

We present an analysis of $\ensuremath{\pi}\ensuremath{\pi}N$ final states obtained from ${\ensuremath{\pi}}^{\ensuremath{-}}p$ interactions at 2.26 GeV/c. Strong $\ensuremath{\rho}$ production is present in both final states. In addition, significant nucleon isobar production is observed. We observed the following cross sections: $\ensuremath{\sigma}({\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}p)=3.77\ifmmode\pm\else\textpm\fi{}0.13$ mb, $\ensuremath{\sigma}({\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n)=5.67\ifmmode\pm\else\textpm\fi{}0.17$ mb, $\ensuremath{\sigma}({\ensuremath{\rho}}^{\ensuremath{-}}p)=2.19\ifmmode\pm\else\textpm\fi{}0.09$ mb, $\ensuremath{\sigma}({\ensuremath{\Delta}}^{+}(1236){\ensuremath{\pi}}^{\ensuremath{-}})=0.30\ifmmode\pm\else\textpm\fi{}0.10$ mb, $\ensuremath{\sigma}({N}^{0}(1650){\ensuremath{\pi}}^{0})=0.49\ifmmode\pm\else\textpm\fi{}0.07$ mb, $\ensuremath{\sigma}({\ensuremath{\rho}}^{0}n)=2.89\ifmmode\pm\else\textpm\fi{}0.11$ mb, $\ensuremath{\sigma}({\ensuremath{\Delta}}^{\ensuremath{-}}(1236){\ensuremath{\pi}}^{+})=0.11\ifmmode\pm\else\textpm\fi{}0.06$ mb, $\ensuremath{\sigma}({N}^{+}(1470){\ensuremath{\pi}}^{\ensuremath{-}})=0.24\ifmmode\pm\else\textpm\fi{}0.06$ mb, and $\ensuremath{\sigma}({N}^{+}(1650){\ensuremath{\pi}}^{\ensuremath{-}})=0.45\ifmmode\pm\else\textpm\fi{}0.05$ mb. The spin-density matrix elements are determined for the ${\ensuremath{\rho}}^{0}$ by interpreting the ${\ensuremath{\rho}}^{0}$ asymmetry as an interference between the resonant $P$ wave and a $T=0$ $S$ wave. A search for the ${\ensuremath{\epsilon}}^{0}$ in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}n$ final state failed to yield a direct observation of this effect.