FRANCK-CONDON CALCULATIONS FOR DOUBLE IONIZATION OF MOLECULAR HYDROGEN

The Franck-Condon radial overlap integral for transition from the ground vibronic state of H2 to a state in the H2++ continuum is expanded as an asymptotic series in powers of a small parameter. The initial semiconvergence of the series is sufficiently rapid to provide a convenient basis for computing the kinetic energy distribution for protons formed by double ionization of H2. The results of these computations are presented. The analysis includes a derivation of the reflection approximation for the particular case of transition to the repulsive Coulomb potential curve. Preliminary results of a more general study indicate that this approximation can be applied to a much larger class of repulsive potentials. Previous forms of the reflection approximation, which have heretofore lacked theoretical foundation, are classified and discussed in relation to the derived approximation.