Relativistic crystal-field radial integrals for rare-earth ions

The purpose of this paper is to indicate the importance of using relativistic self-consistent-field wave functions for the calculation of crystal-field radial integrals. In relativistic calculations the wave functions corresponding to j = l ± 1/2 are different and give different radial integrals. In order to facilitate comparison with nonrelativistic results it is convenient to apply the effective-operator technique in crystal-field calculations as has been done for a long time in hyperfine-structure analysis. In this paper, general formulas are given for the relativistic effective-field Hamiltonian with the corresponding radial integrals. Theoretical values of radial integrals calculated with both relativistic Hartree-Fock and Hartree-Fock-Slater type wave functions are given for Gd3+ and Er3+