Rotational-Vibrational Coupling in the Theory of Electron-Molecule Scattering

The adiabatic-nuclei approximation of vibrational-rotational excitation of homonuclear diatomic molecules can be simply augmented to describe the vibrational-rotational coupling by including the dependence of the vibrational wave function on $j$. Appropriate formulas are given and the theory is applied to $e$-${\mathrm{H}}_2$ excitation whereby it is shown that deviations from the simple Born-Oppenheimer approximation measured by Wong and Schultz can be explained. More important, it can be seen that the inclusion of the $j$-dependent centrifugal term is essential for transitions involving high-rotational quantum numbers.