A self-consistent eikonal treatment of electronic transitions in molecular collisions

Abstract

We develop an eikonal treatment of electronic transitions in many-atom collisions, in which classical nuclear trajectories are self-consistently coupled to quantal electronic transitions. The treatment starts with a discussion of the electronic representations required to assure that Hamiltonian matrices are Hermitian. The amplitudes of wave functions are found to satisfy coupled equations which are expanded in powers of a local de Broglie wavelength. Time-dependent equations are transformed to derive a Hamiltonian formalism that couples nuclear positions and momenta with electronic amplitudes. Cross sections are obtained from flux conservation and also from T-matrix elements.