Use of Relativistic Wavefunctions in Crystal-Field Theory

The purpose of this paper is to indicate some of the consequences of using relativistic wavefunctions in crystal-field calculations. Substitutional expressions are developed which permit the calculation of relativistic crystal-field matrix elements using LS basis states following the method of Sandars. In these expressions the angular parts of the matrix elements are evaluated using LS basis states while the radial part uses the radial integrals computed from relativistic Hartree—Fock-type wavefunctions. It is demonstrated that the crystal-field matrix elements are no longer diagonal in the spin quantum number S when relativistic wavefunctions are used. Recognition of this point leads to an important, and hitherto unnoticed, second-order contribution to the ground-state splitting of S-state ions.