Study of the isospin structure of single-pion production in charged-current neutrino interactions

The isospin structure of weak single-pion production in the reactions $\nu p\to {\mu }^{-}p{\pi }^{+}$, $\nu n\to {\mu }^{-}p{\pi }^0$, and $\nu n\to {\mu }^{-}n{\pi }^{+}$ has been studied using the 7-foot deuterium bubble chamber exposed to a wide-band neutrino beam at BNL. We find that the $I=\frac{1}{2}N\pi$ amplitude is substantial even in the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ mass region and the relative phase angle $\psi$ is approximately 90° as predicted by the Adler model.