Application of the Adiabatic-Nuclei Theory to Vibrational Excitation

The adiabatic-nuclei theory is shown to be quantitatively applicable to vibrational excitation of diatomic molecules by electron impact. When the dependence of the fixed-nuclei phase shifts on internuclear separation is approximated by a two-term Taylor series, the resulting formulas are transparent and easily evaluated. Application to $e-{\mathrm{H}}_2$ excitation is made, phase-shift derivatives are estimated, and the theory is found to fit experimental data.