Calculation of radiative single-charge-transfer cross sections for collisions ofHe2+with He at low energy

A theoretical study of low-energy collisions of ${\mathrm{He}}^{2+}$ with He has been made. Potential curves are obtained using generalized valence-bond wave functions for the $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state formed from ${\mathrm{He}}^{+}$ + ${\mathrm{He}}^{+}$ and the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $E{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states formed from ${\mathrm{He}}^{2+}$ + He. The predominant mechanism for single charge transfer is a radiative transition. The dipole transition moment connecting the $B$ and $X$ states is calculated using the ab initio wave functions. The radiative collision problem is formulated in terms of a complex potential and solved in the JWKB approximation. Cross sections are presented for energies from 0.001 to 10 eV. A rate constant of 3.6 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec at 300 K is obtained. This value is in satisfactory agreement with the recent experimental result and there is some evidence that the remaining discrepancy is due to the effect of tunneling and shape resonances, which have been estimated to increase the rate to 4.4 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec. The splitting of the asymptotically degenerate $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $E{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states is also examined and a conflict with a recent prediction of the asymptotic splitting is resolved.