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

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.

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