Natural rotational quantum numbers for Hunds cases a and b

At low-TV+ and low-ra, Rydberg states typically exhibit a case (b) level pat- 

In the traditional (simplified) case (d) limit, the good quantum numbers are drawn from the partially redundant set, uJSN(Sr) J+N+S+A+sI(sr, Ir), 

Watson (1999) analyzes two subcases of case (d), which he calls (o+,d) and (b+ d). The good quantum numbers in the former are A+5+S+ J+Q+ls(J — sr)J (2S+ + 1 values of ft+) and in the latter subcase A +S+N+J+ls(J — sr)J (2S+ + 1 values of N+). Consider an example in which the ion-core has 1A symmetry, then the nonzero quantum numbers in both (a+,d) and (b+. d) sets of basis functions are reduced to A+N+lsNJ, which is the set of quantum numbers traditionally used to describe a Hund s case (d) Rydberg state. The larger set of quantum numbers, expressed in the form specified by Watson (1999) rather than the more familiar quantum numbers used here, is needed to uniquely specify the transformations between (core, Rydberg) composite cases when S+ 0. 

In case (b) the pattern-forming rotational quantum number is N and the /-uncoupling term, 

All terms in the modified case (b) form of HROT can be evaluated in the case (d) basis set, 

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