Revised Born-Oppenheimer approach and a reprojection method for inelastic collisions

The quantum reprojection method within the standard adiabatic Born-Oppenheimer approach is derived for multielectron collision systems. The method takes nonvanishing asymptotic nonadiabatic couplings into account and distinguishes asymptotic currents in molecular-state channels and in atomic-state channels. The method is demonstrated for the example of low-energy inelastic Li $+$ Na collisions for which the conventional application of the standard adiabatic Born-Oppenheimer approach fails and leads to paradoxes such as infinite inelastic cross sections.