Semiclassical multichannel perturbed-stationary-state model for rearrangement atomic collisions.

Abstract

We present a translationally invariant formulation of the semiclassical perturbed-stationary-state (PSS) method of atomic collisions that satisfies scattering boundary conditions without resorting to the electron translation factor. Our formulation hinges on the fact that correctly dissociating linear combinations of adiabatic electronic states become in the limit proper atomic states. Galilean invariant dynamical couplings are generated by scattering momenta conjugated to reaction coordinates in the Jacobi frames appropriate for describing either the colliding or the parting atomic species. Residual asymptotic couplings exist and constitute a necessary ingredient of our theory. They emerge because an electron in asymptotic capture (charge-exchange) state travels in the Jacobi frame proper for its collision entry state. As such, we do not eliminate the residual couplings by modifying the adiabatic functions with an electron translation factor, but rather harness them to construct asymptotic interaction-picture traveling states suitable for the PSS basis employed. This allows negating the traveling phases from the semiclassically propagated adiabatic amplitudes. The resulting phase-free capture amplitudes reach a definite asymptotic limit. The collision momentum operators in Jacobi coordinates proper for different asymptotic rearrangements are not equivalent. This is always true regardless of the basis employed, since imposing a diagonal internal kinetic energy in one Jacobi frame necessarily implies it is not diagonal in other internal coordinates (which is also the source of residual couplings). We therefore suggest a unique and instantaneous dynamical coupling operator may be constructed as the temporal adiabatic-state weighted average of the scattering momenta associated with the electronic rearrangements spanned by the basis. The proposed multichannel PSS propagator is shown, in forthcoming work, to faithfully reproduce the charge-exchange cross sections in collisions of ${\mathrm{He}}^{2+}$ on H and ${\mathrm{H}}^{+}$ on ${\mathrm{He}}^{+}$ up to the energies where ionization becomes important.