PGOPHER, a program for rotational, vibrational and electronic spectra

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The Rank of the Transition Moment

The Rank of the Transition is derived from the number of photons involved in the transition. For an ordinary absoption or fluorsecence spectrum, only one photon is involved so the rank is one.

For a two photon absorption, as found in multiphoton ionisation, the rank is found by coupling the angular momenta of the individual photons (1) together using the standard angular momentum coupling rules. This gives possible ranks of 0, 1 and 2. The rank 1 component is forbidden by symmetry when the photons are identical, leaving rank 0 or 2. If lambda does not change in the transition, the rank 0 component is often dominant, though both are often seen.

For a three photon transition, ranks of 0 to 3 are possible, though again only ranks 1 and 3 are seen for identical photons.

The rank of the transition gives the maximum possible change in J. There is also a projection of the rank, q, which gives the change in lambda. For a simple absorption spectrum a parallel band has q=0 and a perpendicular transition has q=1. For the simple use of the program here this is automatically worked out from the values of lambda for the ground and excited states. For rank two or higher more than one projection can contribute, which is handled by the full version of PGOPHER

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