The Application of the Correspondence Principle to Degenerate Systems and the Relative Intensities of Band Lines

Abstract

Relative intensities of band lines of a diatomic molecule according to the correspondence principle.—This paper originated in an attempt to harmonize the Kratzer half integral quantum numbers, for which there is strong evidence, with the observed symmetry in the intensities of the two branches of the HCl band at 3.46μ. First the infra-red spectrum of non-gyroscopic diatomic molecules is calculated, treating the molecule as a degenerate system with but one quantum condition for two degrees of freedom, following the detailed rules proposed by Kramers. This leads to a formula for the relative intensities of the lines in the two branches of the band which is unsymmetrical and disagrees with the experimental observations. The theoretical intensity (i.e. integral absorption coefficient) of the first line of the positive branch is more than twice that of the first line of the negative branch. This dissymmetry may be greatly reduced if the a priori probability of the upper quantum level, which appears as a factor in the intensity formula, is replaced by the mean of the a priori probabilities of the initial and final states. Such a modification of the theory is justified by a recalculation of intensities, treating the molecule as a non-degenerate system, e.g., one whose orbits are quantized in space under the influence of a weak magnetic field. A comparison between the theory and experiment involves the computation of the total absorptions to be expected in a tube of appreciable length using a relatively wide slit. It this computation is based on the assumption that the lines have no unresolved fine structure, the estimated absorptions do not agree with experiment, but the assumption that such a fine structure does exist, combined with the integral absorption coefficients of the modified theory, gives fair agreement with the available observations. General theory of transition probabilities. It is pointed out that the usual method of calculating probabilities involves a discontinuity in the intensities of spectrum lines when a degenerate system is converted into a non-degenerate one, as by a weak magnetic field. This seems improbable and the failure of the first calculation indicates that the usual rules for the treatment of degenerate systems require modification.