Role ofρ2term in pion-nucleus dynamics

We study the corrections to the first-order optical potential in $\pi$-nucleus elastic scattering from 28 to 260 MeV. The dynamical effects of true pion absorption (and correlations) are incorporated into our analysis through the inclusion of a second-order optical potential. We have performed a ${\chi }^2$ fit to the measured $\pi -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ and $\pi -{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic differential cross sections in order to determine a parametrization of the second-order optical potential. It is shown that the inclusion of these higher-order effects not only yields excellent fits to the low-energy data (50 MeV), but also systematically improves calculated cross sections at the larger angles in the resonance region. We also find a general improvement in the agreement between the calculated and measured total cross sections, in particular at low energies. Since our first-order potential is essentially parameter free, we believe that the parameters of the second-order potential determined from the present work are meaningful and may serve as a useful guide in future microscopic analyses.