Herman-Wallis expansion for intensities

Intensities of transition can be also analyzed by means of fitting formulas. An expansion quite often used for infrared transitions is the Herman-Wallis (1955) form 

The quantity m in Eq. (1.74), which should not be confused with the projection of the angular momentum / on the z axis, is given by 

One can see by comparing with Eq. (1.45) that m is the line strength Sh For the Morse potential, and in lowest approximation, Fv v(m)= 1 and is given by the formulas of Section 1.7. 

The material in this section is discussed in all texts of quantum mechanics. A very useful compilation of explicitly solved examples is Fliigge (1971). See also the very good but not so easily available collection of problems of Gold man et al. (1960). 

More elementary introductions to the material in the rest of this section can be found in Messiah (1976) or Cohen-Tannoudji, Diu, and Laloe (1977). More detailed discussions are available in Fano and Racah (1959), Edmonds (1960), Brink and Satchler (1968), de Shalit and Talmi (1963), and Judd (1975). Zare (1988) is particularly useful on both the theory and the manner of its application. Special reference to diatomic molecules is made by Judd (1975) and Mizushima (1975). The close connection to Lie algebra is emphasized by Biedenham and Louck (1981). A summary of the results we need is in Appendix B. 

---