Low-energy ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, ${\mathrm{Xe}}^{+}$ + K, Rb, Cs charge-transfer total cross sections

Asymmetric charge-transfer total cross sections have been calculated for the reaction $X^{+}+\mathrm{Alk}\to X^{*}+{\mathrm{Alk}}^{+}$, where $X$ represents Ar, Kr, or Xe and Alk represents K, Rb, or Cs. The calculations were performed at low velocities, $v\sim 1\times {10}^6$ cm/sec, using a modified method of Demkov and semiempirical coupling matrix elements. The Ar results are compared with the experimental data of Peterson and Lorents and agreement is found in the total cross-section shape, but there is an increasing underestimation of the cross section with the higher-atomic-weight alkali-metal atoms. This problem is attributed to the importance of rotational coupling to the $p$-state levels of the excited noble-gas products, suggesting more accurate cross sections for Kr and Xe, where the contribution from the $p$ states will be of lesser importance. Large cross sections are predicted for direct production of the metastable noble gas in the lowest-lying ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state for the reactions ${\mathrm{Ar}}^{+}$ + Rb, ${\mathrm{Kr}}^{+}$ + Rb, and ${\mathrm{Xe}}^{+}$ + Cs.