Thoery of level splitting: Spectrum of the octahedrally invariant fourth-rank tensor operator

Abstract

The theory of level splitting of certain vibration-rotation states (including the ground state) in spherical-top molecules is developed within the framework of the standard Racah-Wigner tensor algebra, thus demonstrating the direct applicability of these general techniques without making the usual modifications associated with the anomalous commutation relations of the body-fixed angular momentum components. The eigenvalue spectrum of the octahedrally invariant fourth-rank tensor operator is examined in detail, and the unexpected periodic symmetry and asymptotic degeneracy features of the spectrum are described.