Evidence for the quasifree character of the (π±,πN) reactions onC12,Mg24, andCa40

Cross sections for (${\pi }^{\pm }$,$\pi N$) reactions near the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ resonance on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ leading to mirror levels in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$/${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$/${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$/${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, respectively, were measured by observing their $\gamma$ decays. $\frac{{\sigma }_n}{{\sigma }_p}$ for the first $\frac{1}{2^{-}}$ levels in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$/${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ is 1.4±0.2 for ${\pi }^{-}$ and $\frac{1}{1.8}\pm 0.2$ for ${\pi }^{+}$. For ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$/${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$/${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, the ratios are generally not as closely reciprocal as for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and the previously reported ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$/