Configuration interaction in rare earth ions

Abstract

An analysis is given of the interaction between the electronic configurations (nl)N(ńl')4l'+2 and (nl) N(n'l') 4l'+1(n"l"), and of the way it affects the matrix elements of a single-particle double-tensor operator T (κk). The theory is applied to rare earth ions, for which nl ≡ 4f. It is shown that the infinite sums that occur in the calculation of the corrections to the spin-orbit coupling due to this kind of configuration interaction can be related to the corresponding sums that occur when the corrections to the orbital part of the magnetic hyperfine interaction are analysed. Deviations between theoretical and experimental values of the spin-orbit coupling constant for rare earth ions are used to estimate the adjustments that should be made to 〈1/r3〉 when calculating the magnetic hyperfine interaction. The effective values of this quantity thus obtained are found to be in excellent agreement with experiment. Some discussion is given of the calculation of the analogous adjustments to 〈1/r 3〉 for the quadrupole interaction.