Microwave Zeeman Effect and Theory of Complex Spectra

A treatment in spherical tensors of the microwave Zeeman interaction of Abragam, Kambe, and Van Vleck is given. A calculation of $g$ factors in atomic oxygen is then made and the numerical values compared with those worked out previously. New methods and results are developed for finding matrix elements of one-particle and two-particle operators for wave functions which contain more than one group of equivalent particles. The generality of these results is such that they may be used in the various coupling schemes of atomic and nuclear shell models.