Crystal Electric Fields for Cubic Point Groups

Crystal electric fields for the cubic point groups are reexamined and it is found that the new term O 6 2 - O 6 6 is nonvanishing for the cubic point groups T h and T due to the lack of Umklappung and fourfold symmetry axis of the point group O h . The eigenfunctions and eigenvalues of the crystal electric field for 4 f n configurations are labeled by the irreducible representations of the point group T h . The degeneracy of each sublevel does not change as compared with those of the point group O h , but some eigenfunctions and eigenvalues are affected by the new term. Thus inelastic neutron scattering spectra for T and T h are different from those for O h due to different transition probabilities and selection rules.