Time-dependent many-electron approach to slow ion-atom collisions: The coupling of electronic and nuclear motions

We describe the coupling of electronic and nuclear motions in slow atomic collisions using a combination of the eikonal and time-dependent Hartree-Fock (TDHF) approximations. Starting with an eikonal representation of the total wave function, a wave function is constructed from classical trajectories in a way suitable for describing atomic collisions with velocities down to a fraction of an atomic unit. The TDHF formulation is developed in terms of its density operator. The differential equations coupling the density operator to the nuclear motions have been solved with a procedure developed to account for the coupling of fast (electronic) and slow (nuclear) degrees of freedom. This is based on a local-interaction picture and on a temporal linearization of the equations, allowing for the integration of the electronic density over large time intervals. Density-matrix equations are derived in a basis of traveling atomic orbitals, and numerical results are presented for ${\mathrm{H}}^{+}$+H and ${\mathrm{He}}^{2+}$+H. Good agreement is found with experimental results for ${\mathrm{H}}^{+}$+H, comparing integral electron transfer cross sections from 2 to 2000 eV. In addition, an analysis of the time dependence of atomic orbital populations provides insight on electronic rearrangement during collisions and shows that even very small contributions from the driving forces of the nuclei on the electrons have a cumulative effect on the density operator that can substantially change final populations.