Charge-transfer process using the molecular—wave-function approach: The asymmetric charge transfer and excitation in Li +Na+and Na +Li+

Abstract

The charge-transfer processes occurring in collisions of Li + ${\mathrm{Na}}^{+}$ and Na + ${\mathrm{Li}}^{+}$ have been studied theoretically using the molecular-wave-function approach. The wave functions and Born-Oppenheimer breakdown terms were evaluated using rigorous methods. The six lowest molecular states (dissociating to the $2s$ and $2p$ atomic states on Li and to the $3s$ and $3p$ atomic states of Na) were included in the coupled equations. The transition probabilities were calculated using linear trajectories for a variety of impact parameters and ion velocities. We find that the over-all transition processes are well represented as a succession of simple two-state transition processes ($\Sigma -\Sigma$, $\Sigma -\Pi$, and $\Pi -\Pi$). The $\Sigma -\Sigma$ two-state process can be described in terms of three steps involving (i) a coupling region as the atoms come together [$\mathrm{}(10-20)\mathrm{}{a}_0$], (ii) an uncoupled phase changing region for shorter separatons ($<10\mathrm{}{a}_0$), and (iii) a decoupling region as the atoms depart [$\mathrm{}(10-20)\mathrm{}{a}_0$]. On the other hand, in the molecular—wave-function formulation, the $\Sigma -\Pi$ two-state transition process involves continuous coupling (for $R<\mathrm{}7\mathrm{}{a}_0$). As a result the transition probabilities for $\Sigma -\Pi$ coupling differs from that of $\Sigma -\Sigma$ coupling, leading to rather different forms for the cross sections.