Interrelationships between Intensity Factors

The relationships between measurable quantities related to absolute transition probability (e.g. absorption cross section, molar absorption or extinction coefficient, radiative lifetime) and the fundamental quantities used to describe and inter-relate the observable quantities axe fraught with difficulties of unit conversions and internally consistent treatments of initial- and final-state degeneracies. Several excellent papers on this subject exist (Hilborn, 1982 and 2002, Larsson, 1983, Tatum, 1967, Schadee, 1978, and Whiting, et al., 1980). Much of Section 6.1.1 is based on or checked against Hilborn (1982 and 2002), although slightly different notation and definitions are used. 

It is a well established convention in spectroscopy to describe a transition by specifying the quantum numbers of the upper state first, regardless of whether the upper state is the initial or final state of the observed transition. It is not possible to follow this convention in defining most of the quantities that specify the absolute strength of a transition. The reason for this is the necessity to include initial and/or final state degeneracy factors g-i and p/) in the definitions of some of the measures of transition strength. 

There axe a variety of properties related to transition intensities that can be affected by perturbations. The most important of these are the following isolated-molecule quantities. 

Transition moment for electric dipole transitions (in the dipole length approximation) is defined as, 

Radiative lifetime, Ty is a property of a single level, whereas py describes a transition between two levels. 1 /r is the rate at which the population of level 

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Whiting, et al., 1980). Definitions and interrelationships between intensity factors are given by Hilborn (1982 and 2002), Tatum (1967), Whiting and Nicholls (1974), and Schadee (1978). The definitions of transition moments and intensity factors suggested by Whiting, et al., (1980) are adopted in this chapter, except in Sections 6.3 and 6.4 where the factorization of Eq. (6.1.20) is not possible. 

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