Spectra of tensor operators adapted to nonstandard basis. Qualitative features of clustering

Spectra of irreducible tensor operators for the chain of group G ? O(3) are investigated from the qualitative point of view. Conditions are found for clustering of the eigenvalues of tensor operators in the high-J limit. Approximate formulas are proposed which permit the calculation of the relative positions of the clusters. Centrifugal distortion of spherical tops, crystal-field splitting, and low-frequency bending vibrations of nonrigid molecules composed of an atom and rigid symmetrical core are considered as physical examples. Clustering of the F^(kJJ′) coefficients of Moret-Bailly are qualitatively explained as well.