Study of the Reactionπ−p→π+π−nat an Incident Energy of 870 MeV

In the reaction ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$, we have measured the ${\pi }^{+}$ momentum spectrum at various angles, from which the distributions ${\left(\frac{d^2\sigma }{\mathrm{dMd}\Omega }\right)}^{*}$ of the ${\pi }^{-}n$ system have been deduced. These distributions are compared with those obtained from a phenomenological model. This comparison allows a determination of the amplitude of the inelastic waves. It is found that the resonant waves $D_{15}$ and $F_{15}$ are not strongly coupled to the channel $\Delta \mathrm{}\left(1238\right)+\pi$.