New symmetry properties of the cubic rare-earth centers in crystals

A method that gives analytical basis functions for the irreducible representations which label the crystal field levels of the rare-earth ions in cubic symmetry, regardless how many times these representations enter in the decomposition of the irreducible representation of the three-dimensional rotation group is presented. The method makes use of the transformation properties of the wavefunctions under rotations around two fourth-order axes of the cube and gives analytical crystal field wavefunctions versus the composition parameter of the cubic crystal field potential.