Single-electron excitation and transfer in collisions of alkali-metal and oxygen atoms

An approximate theory is given for calculating the cross sections for single-electron excitation and transfer from a neutral alkali-metal atom $M$ colliding with atomic oxygen. The trajectories of the colliding atoms are computed classically, and the electron is treated by the time-dependent Schr\"odinger equation in two- and three-state approximations. The three states considered are the ground and first-excited states $M$ and ${M}^{*}$ of the incident atom and the single bound state of ${\mathrm{O}}^{\ensuremath{-}}$. Numerical calculations are carried out for energies between 10 and 10 000 eV (laboratory energies of the alkali-metal atoms). Comparison of results obtained with the two- and three-state approximations shows that the charge-transfer cross sections are almost unaffected by the presence of the alkali-metal-atom excited state. The excitation cross sections, on the other hand, are considerably increased by the presence of the ionic channel. This evidence indicates that excitation can occur as a two-step process in which the electron is exchanged between the colliding partners. The numerical values of the electron-transfer cross section generally agree with those calculated by van den Bos for Cs-O collisions (based on the Landau-Zener-St\"uckelberg theory and suitably corrected by a statistical weight factor) and the recent experimental data of Woodward. At low velocities ($v<0.01$ a.u.), however, we find a steeper decrease with decreasing velocity than the Landau-Zener-St\"uckelberg results. At high velocities the results agree with the Born approximation.