We calculate the cross section for the double charge exchange (DCE) reaction (${\pi }^{+}, {\pi }^{-}$) The multiple-scattering series for DCE scattering of pions by nuclei is found to converge slowly. To take into account the higher order contributions, we use an eikonalized distorted wave formulation, which is obtained from the usual Glauber series by retaining those terms corresponding to coherent scattering processes. We include $s$, $p$, $d$, and $f$ partial waves in the pion-nucleon ($\pi N$) elastic scattering amplitudes used in the calculations. Our results show that for incident pion energies below ∼200 MeV the contribution of the spin-flip part of the $\pi N$ elastic scattering amplitude to the cross section interferes significantly with that due to the spin-independent part of the $\pi N$ amplitude. The $d$ wave of the $\pi N$ amplitude contributes significantly to the cross section above ∼100 MeV. Above ∼500 MeV the contribution from the $f$ wave becomes important. The calculated total DCE cross section for ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({\pi }^{+}, {\pi }^{-}){}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ has a minimum near 130 MeV. Although a maximum occurs near the (3,3) resonance energy in both the double scattering and the double plus triple scattering cross sections, in the full distorted wave results the maximum is located near 400 MeV and is rather broad. The forward differential cross section for DCE exhibits the same qualitative features as the integrated cross section as a function of the pion incident energy. The angular distributions are peaked in the forward direction and possess structure in the form of maxima and minima or shoulders.

NUCLEAR REACTIONS ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({\pi }^{+}, {\pi }^{-}){}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$, $E\le 550$ MeV; calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, $\sigma (E, \theta =0\mathrm{}°)$, $\sigma \left(\theta \right)$.

• Received 24 September 1974

DOI:https://doi.org/10.1103/PhysRevC.11.760