Electron transfer and spin-flip processes in atom-atom collisions from variationally improved time-dependent Hartree-Fock results

A variational functional for transition amplitudes is applied to atom-atom collisions using a time-dependent formalism. The transition amplitude is a functional of two independent trial wave functions with specified initial and final conditions, respectively. Transition probabilities are obtained by evaluating the functional in terms of standard time-dependent Hartree-Fock (TDHF) trial functions. The TDHF method is implemented by expanding the molecular orbitals as linear combinations of traveling atomic orbitals. The procedure requires no other molecular integrals than those needed to construct the Fock operator. The present method is applied to He+${\mathrm{He}}^{2+}$ and ${\mathrm{H}}^{+}$+${\mathrm{He}}^{+}$ collisions with specified nuclear trajectories using a minimal atomic-orbital basis set. Within this model an exact, close-coupling-type solution is also feasible, and has been obtained for comparison purposes. Numerical values of probabilities and of cross sections obtained from the variational functionals for elastic, spin-flip, and one- and two-electron transfer processes show substantial improvements over the standard TDHF results.