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 ${\text{1sσ2sσ}}^3{\Sigma }_g$ and the ${\text{1sσ2pσ}}^3{\Sigma }_u$ 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 impact from the ground state, upon the basis of an extension of the Franck‐Condon method. The spectral intensities so obtained are compared with those given by several forms of approximate calculation, and the discrepancies critically discussed. Comparisons are also made with the experimental work of Smith and of Finkelnburg and Weizel. It is concluded that the Franck‐Condon principle leads to results definitely incompatible with their observations. Indications are found that other transitions than the one treated in this work are contributing appreciably to the radiation observed by Smith. An analysis of the spectrum observed by Finkelnburg and Weizel leads to a critical discussion of the method used by them in deducing the potential curve of the repulsive state, from which is drawn the conclusion that this curve is without quantitative significance.