Intermediate-energy pion-nucleus scattering assuming a separable fixed-scatterer pion-nucleon interaction

A formal discussion of the optical potential due to Foldy and Walecka is extended to include spin and isospin degrees of freedom and projectile relativistic kinematics. The formalism is applied to intermediate-energy pion-nucleus elastic scattering. Assuming an infinitely heavy nucleon mass, we obtain a fixed-scatterer separable-potential parametrization of the two-body pion-nucleon scattering data in the laboratory system. This effective two-body potential is used in a consistent manner as microscopic input in the many-body pion-nucleus elastic scattering problem. Using the approximations adopted by Foldy and Walecka, we obtain a pion-nucleus optical potential which is then applied to study pion elastic scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Total cross-section and angular-distribution predictions for pion kinetic energies $\sim 70-280$ MeV are presented. Good agreement is obtained with the available experimental data on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$.