Differential elastic-scattering measurements ofXe+on Xe andAr+on Ar in the 20-340-eV range

Relative measurements of the differential cross section for elastic scattering of ${\mathrm{Xe}}^{+}$ on Xe and ${\mathrm{Ar}}^{+}$ on Ar are reported in the energy range 20-340 eV and the angular range 1-15 deg (lab). The data are presented in terms of the reduced cross section $\rho \left(\theta \right)\equiv \theta sin\theta \sigma \left(\theta \right)$ and the reduced angle $\tau \equiv E\theta$. The $\rho -\mathrm{v}\mathrm{s}-\tau$ plots for ${\mathrm{Xe}}^{+}$ on Xe show complex oscillations which we attribute primarily to phase interference in scattering from three coherent pairs of gerade-ungerade potential curves. The six states involved are the electronic fine-structure states of $\mathrm{Xe}_2^{}{}_{}{}^{+}$, four of which dissociate to $\mathrm{Xe}+{\mathrm{Xe}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)$, and the other two to $\mathrm{Xe}+{\mathrm{Xe}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$. At larger values of $\tau$ the elastic scattering pattern is further complicated by potential-curve crossings and excitation to higher states, while at smaller $\tau$ potential wells give rise to two rainbow peaks. We have resolved two oscillatory patterns in the data, from which we have determined two difference potentials for $\mathrm{Xe}_2^{}{}_{}{}^{+}$, $\Delta V_{\mathrm{JM}}\mathrm{}\left(R\right)\mathrm{}\equiv \left|V_{\mathrm{JMg}}\mathrm{}\right(R)-V_{\mathrm{JMu}}\mathrm{}(R\left)\right|:\Delta V_{\frac{3}{2},\frac{3}{2}}=23\mathrm{}{e}^{-1.23R}$, $3.5\lesssim R\lesssim 5.5$; and $\Delta V_{\frac{1}{2},\frac{1}{2}}=2.0\mathrm{}{e}^{-0.788R}$, $5\lesssim R\lesssim 6.5$, in a.u. The ${\mathrm{Ar}}^{+}$ on Ar data are in excellent agreement with scattering calculations based upon ab initio computations of the ${\Pi }_u$ and ${\Pi }_g$ potentials of $\mathrm{Ar}_2^{}{}_{}{}^{+}$.