Theory of the Hyperfine Structure of Molecules: Application to 3Π States of Diatomic Molecules Intermediate between Hund's Cases (a) and (b)

Abstract

In order to fully utilize the experimental accuracy of the high resolution afforded by radio‐frequency spectroscopy, a fourth‐order treatment of the energy is required. Especially, this fourth‐order treatment is expected to be necessary in order to separate the quadrupolar interactions of light atoms in molecules from pseudoquadrupolar contributions to the energy due to magnetic hyperfine interactions which are off diagonal in the rotational state. The example of ³Π states intermediate between Hund's Cases (a) and (b), where J is still a good quantum number, is chosen to demonstrate the general techniques of such a fourth‐order calculation. (Particular reference is made to the a ³Π state of isotopically substituted CO.) Van Vleck's method of reversed angular momentum is generalized to spherical tensor form in anticipation of future needs in the calculation of hyperfine structures of more complex systems. The spectroscopic parameters are explicitly written as matrix elements of the nonrelativistic wavefunctions in order that they be usable as checks on approximate molecular wavefunctions. Second‐order Stark and Zeeman effects are also discussed.