On the Franck—Condon Factor for Continuous Spectra

The Franck—Condon factor for a continuous absorption spectrum has by semiclassical consideration the shape of the ground state density probability function. It is shown here that the very deviation from the semiclassical approach introduces additional peaks as well as asymmetries into the continuous spectra. An approximate formula for the Franck—Condon factor for the transition from the v=0 state of a diatomic molecule into a continuum is given, where the repulsive potential appears explicitly. The approximation is then investigated both analytically and numerically, and quantititative examples for the O2 molecule are given.