Experimental Test of the Franck-Condon Principle: Double Ionization of Molecular Hydrogen

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Abstract
The double ionization of molecular hydrogen by electron impact has been observed by coincidence detection of the resulting proton pairs in a system especially designed for absolute kinetic energy measurements. Monte Carlo calculations provided an accurate knowledge of the resolution with which the kinetic energy measurements were made. Experimental results agree closely with predictions based on accurate Franck‐Condon overlap integrals for a model involving Morse oscillatorwavefunctions for the molecule and Coulomb wavefunctions for the ion. In contrast, the reflection approximation and the harmonic oscillator approximation for molecular vibration, two approximations frequently made in such Franck‐Condon calculations, do not agree well either with experiment or accurate calculations. Observations at electron energies of 0.5, 0.75, and 1 keV show that the kinetic energy distribution is independent of electron energy and suggest that the double ionization cross section is inversely proportional to electron energy in this range. These results are to be expected for a direct two‐electron ejection mechanism for double ionization of H2.