Rotation matrix elements and further decompositionfunctions of two-vector tesseral spherical tensor operators; theiruses in electron paramagnetic resonance spectroscopy

Abstract

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