Rotation matrix elements and further decomposition functions of two-vector tesseral spherical tensor operators; their uses in electron paramagnetic resonance spectroscopy

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Abstract
Matrix elements, Ag,h(k) (k = 1-6), which describe a general Euler angle transformation of coordinates to which tesseral spherical tensor operators, k,q, are referred have been calculated and extended to include matrix elements for odd k. The matrix elements have been incorporated into a general axis-transformation computer program which relates to parameter sets in any one of the more commonly used tesseral forms, namely, conventional Stevens, normalized Stevens (Racah normalization) and normalized spherical tensor (Koster and Statz normalization) operators. Tables of decomposition functions of tesseral spherical tensor operators, k,q(B,J) ( J = S,I ), are extended to detail decompositions for terms of dimension BJ7 and, implicitly, for decomposition of any two vector operators k,q(V,W) to experimentally usable single vector forms where VkVWkW (one of kV, kW unity) is the dimension of a general term in the decomposition. Tables detailing the symmetry-allowed terms under the 11 Laue (site) crystal classes are also extended to include tesseral tensorial sets up to rank 8, thus including the new terms. The use of these functions to describe electron paramagnetic resonance studies of high-spin nuclear Zeeman interactions is discussed.

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