Theory of spin-orbit coupling in atoms, II. Comparison of theory with experiment

Abstract Results of calculations of the spin-orbit coupling constant for 2p, 3p, 4p, and 3d shell ions and atoms are presented. The calculations are based on a theory developed in a previous paper. Excellent agreement of this theory with experiment is obtained for the 2p and 3d shell ions, while calculations using the familiar ∂V/r∂r expression for the coupling constant lie 10 to 20 % too high. The exchange terms discussed in the earlier paper make a contribution to the coupling constant of the same sign and order of magnitude as the ordinary shielding terms. For the 3p and 4p shell atoms, the calculated coupling constants based on the exact theory and on the ∂V/r∂r expression both tend to lie below the experimental values. An explanation for this disagreement is suggested, based on the noded nature of the outer-electron radial wave functions for these atoms. The importance of the residual-spin-other-orbit interaction is discussed, and it is shown that ignoring the form of this interaction may lead to a large variation in the coupling constant within a configuration.