Elastic pion-nucleus scattering is treated using a separation in Hilbert space via a projection-operator formalism. The basic assumption is that the elastic scattering and reactions due to the $\pi -N$ resonance proceed through doorway states consisting of a $\Delta \mathrm{}\left(1236\right)\mathrm{}$ resonance in the nucleus. Nonresonant scattering and absorption processes are included by background terms, which are approximately known. The formalism is applied to ${\pi }^{-}-{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ scattering.

• Received 12 March 1973

DOI:https://doi.org/10.1103/PhysRevLett.30.1071