We consider pion-nucleus elastic scattering and single- and double-charge-exchange scattering to isobaric analog states near the (3,3) resonance within an isospin invariant framework. We extend previous theories by introducing terms into the optical potential $U$ that are quadratic in density and consistent with isospin invariance of the strong interaction. We study the sensitivity of single and double charge exchange angular distributions to parameters of the second-order potential both numerically, by integrating the Klein-Gordon equation, and analytically, by using semiclassical approximations that explicate the dependence of the exact numerical results to the parameters of $U$. The magnitude and shape of double charge exchange angular distributions are more sensitive to the isotensor term in $U$ than has been hitherto appreciated. An examination of recent experimental data shows that puzzles in the shape of the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({\pi }^{+}, {\pi }^{-}){}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ angular distribution at 164 MeV and in the $A$ dependence of the forward double charge exchange scattering on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ at the same energy may be resolved by adding an isotensor term in $U$.

NUCLEAR REACTIONS Scattering theory for elastic, single-, and double-charge-exchange scattering to IAS in the region of the $P33\mathrm{}$ resonance. Second-order effects on charge-exchange calculations of $\sigma (A, \theta )$.

• Received 8 November 1982

DOI:https://doi.org/10.1103/PhysRevC.27.1647