Nuclear charge-exchange corrections to leptonic pion production in the (3, 3)-resonance region

We discuss nuclear charge-exchange corrections to leptonic pion production in the region of the (3, 3) resonance, both from a phenomenological viewpoint and from the evaluation of a detailed model for pion multiple scattering in the target nucleus. Using our analysis, we estimate the nuclear corrections needed to extract the ratio $R=\frac{\left[\sigma \right({\nu }_{\mu }+n\to {\nu }_{\mu }+n+{\pi }^0)+\sigma ({\nu }_{\mu }+p\to {\nu }_{\mu }+p+{\pi }^0\left)\right]}{2\sigma ({\nu }_{\mu }+n\to {\mu }^{-}+p+{\pi }^0)}$ from neutral-current search experiments using ${}_{13}{}^{}{}_{}{}^{}\mathrm{Al}_{}^{27}{}_{}{}^{}$ and other nuclei as targets.