Deviations from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>LS</mml:mi></mml:math>Coupling in the Spheroidal Core Nuclear Model

Abstract

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 $L=I\ensuremath{-}\frac{1}{2}$ and ${L}^{\ensuremath{'}}=I+\frac{1}{2}$ components in Bohr's strong coupling wave function. The orbital gyromagnetic ratio of each component is also determined.Numerical results on the energy displacements produced by the coupling of the odd nucleon to the distorted core are generally unfavorable to the strong coupling description. A perturbation method appropriate to a weak coupling description is more likely to provide a satisfactory solution of the dynamical problem.