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

Matrix elements, A_g,h^(k) (k = 1-6), which describe a general Euler angle transformation of coordinates to which tesseral spherical tensor operators, ℑ_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, ℑ_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 ℑ_k,q(V,W) to experimentally usable single vector forms where V^k_VW^k_W (one of k_V, k_W 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.