Pion elastic and inelastic scattering on s-d shell nuclei in the ${\Delta }_{33}$-resonance region. Coupled-channel analysis

Equations of the coupled-channel method are solved in momentum space for pion scattering on ${}_{}{}^{24}{}_{}{}^{}$,26Mg and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ in the ${\Delta }_{33}$-resonance region. The elastic and inelastic differential cross sections are calculated by using the nuclear ground-state and transition densities which correctly describe the (e,e’) data for the same nuclear states. Also calculated are the double-analog double-charge-exchange reactions ${}_{}{}^{26}{}_{}{}^{}({\pi }^{+}$,${\pi }^{\mathrm{-}}$)${}^{26}$ Si and ${}_{}{}^{18}{}_{}{}^{}({\pi }^{+}$,${\pi }^{\mathrm{-}}$)${}^{18}$ Ne, and the results obtained are in surprisingly good agreement with the experimental data. From the comparison of our coupled-channel and distorted-wave impulse approximation results we conclude that the multistep mechanisms play a minor role in the reactions considered.