Momentum-space second-order optical potential for pion-nucleus elastic scattering

For use in applications such as pion photoproduction and inelastic exclusive pion scattering studies, a first-plus-second-order pion-nucleus optical potential is constructed by fitting the phenomenological ${\rho }^2$-dependent term to the ${\pi }^{\pm }$ ${\mathrm{-}}^{12}$C total and differential cross sections. It is demonstrated that such a potential is A universal (A is the atomic mass number) and well describes all available (total and elastic differential) pion scattering data for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ targets in a broad energy range 14≤$T_{\pi }$≤250 MeV.