Analysis of low energy ${\mathrm{\pi }}^{+}$ scattering to second ${\mathrm{O}}^{+}$ states

An optical potential with a strong Ericson-Ericson-Lorentz-Lorenz parameter is used to calculate low-energy pion inelastic scattering to selected collective states and excited $0^{+}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The nuclear structure input is carefully evaluated, and there are no free parameters in the calculation. The scattering to the $0_2^{+}$ states proceeds dominantly through the one-step mechanism, but the two-step mechanism is significant and can be used to extract some information about the form factors connecting excited states.