Invariant potential for elastic pion-nucleus scattering

From the Wick-Dyson expansion of the exact propagator of a pion in the presence of a nucleus, an invariant potential for crossing symmetric elastic pion-nucleus scattering is obtained in terms of a series of pion-nucleon diagrams. The Chew-Low theory is used to develop a model in which the most important class of diagrams is effectively summed. Included in this model is the exclusion principle restriction on the pion-bound nucleon interaction, the effects of the binding of nucleons, a kinematic transformation of energy from the lab to the $\pi N$ center of mass frame, and the Fermi motion and recoil of the target nucleons. From a numerical study of the effects of these processes on the $\pi -{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ total cross section, the relative importance of each is determined. Other processes contributing to the elastic scattering of pions not included in the present model are also discussed.