Deviations fromLSCoupling in the Spheroidal Core Nuclear Model

Deviations of measured magnetic moments from the Schmidt limits have been interpreted in terms of a failure of $\mathrm{LS}$ coupling. The model of an odd nucleon coupled to a nonspherical core provides an unforced theoretical basis for this interpretation. Projection operators for pure $\mathrm{LS}$ coupling states are introduced and applied to compute the statistical weights of the $L=I-\frac{1}{2}$ and $L^{\prime }=I+\frac{1}{2}$ components in Bohr's strong coupling wave function. The orbital gyromagnetic ratio of each component is also determined.