NEW SYMMETRY PROPERTIES OF THE CUBIC RARE-EARTH CENTERS IN CRYSTALS

A method that gives analytical basis functions for the irreducible rep resentations which label the crystal field levels of the rare-earth io ns in cubic symmetry, regardless how many times these representations enter in the decomposition of the irreducible representation of the th ree-dimensional rotation group is presented. The method makes use of t he transformation properties of the wavefunctions under rotations arou nd two fourth-order axes of the cube and gives analytical crystal fiel d wavefunctions versus the composition parameter of the cubic crystal field potential.