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A method is given for calculating the coupling between the nuclear and electronic motion in the hydrogen molecule ion using the exact wave functions. Calculations are carried out for the transition 1sσ—2sσ and compared with values obtained from simple approximate methods. Estimates are made of the cross sections for excitation and capture into the 2s state during a proton-hydrogen atom collision, using approximate H2+ wave functions to describe the state during collision. Finally, it is shown that a Born-Oppenheimer separation carried out in relative coordinates should be slightly more accurate than the usual treatment using fixed space coordinates. Two different types of relative coordinates suggest themselves for use at different ranges of internuclear separation.
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Jepsen et al. (1960) studied this question.