A Study of the Franck‐Condon Principle

The validity of the Franck‐Condon principle has been investigated in connection with its application to the calculation of spectral intensities in the continuous radiation due to the transitions between the 1sσ2sσ 3Σg and the 1sσ2pσ 3Σu states of H2. For the latter state, a potential curve was constructed on the basis of the authors' theoretical calculations. For the former state, a curve was computed from spectral data by Dunham's method. Accurate wave functions for both states were determined by mechanical integration with the differential analyzer. Transition probabilities from the first four vibrational levels of the stable state were determined by mechanical integration, both for the case that the electric moment matrix element is constant (as assumed in the Franck‐Condon method) and for the case that it is a linear function of the nuclear separation. In addition integrals were determined which permitted the calculation of the probability of excitation of the several vibrational levels by electron im...