Theoretical intensities and selection rules

The intensity of an electric dipole transition in absorption or emission depends, on one hand, on factors particular to the experiment measuring the intensity, e.g., the number density of molecules in the initial state of the transition and, for absorption experiments, the absorption path length and the intensity of the incident light. On the other hand, the intensity involves a factor independent of the experimental parameters. This factor, the line strength 5(f — i), determines the probability that a molecule in the initial state i of the transition f — i will end up in the final state f within unit time. 

If we assume that the initial state i and the final state f are both non-degenerate, then the line strength of the electric dipole transition between them [3] is given by 

As in Ref. [1], we describe the molecule in a space-fixed (or laboratory-fixed) axis system XYZ, and is the component of the molecular dipole moment along the axis A—X, Y, or Z. The complete internal wavefunctions of the initial and final states are written as 10 and 10, respectively. In the present work, we take the 

Inserting the wavefunction from equation (2) in the matrix element square of equation (1), we obtain 

As mentioned above, we assume that the molecular energy does not depend on the nuclear spin state For the initial rovibronic state Peiec) Prv) we have gns nuclear spin functions available, for which the product function 4 i) in equation (2) is an allowed complete internal state for the molecule in question, because it obeys Fermi-Dirac statistics by permutations of identical fermion nuclei, and Bose-Einstein statistics by permutations of identical boson nuclei (see Chapter 8 in Ref. [3]). By necessity [3], the same nuclear spin functions can be combined with the final rovibronic state form allowed complete 

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