Energy levels of paramagnetic ions: Algebra. II

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Abstract
The correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented. The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the Clebsch‐Gordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applied to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the Appendix.

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