Spin–orbit interactions in free lanthanide (3+) ions

The effective nuclear charges of free Ln3+ ions (Ln IV in spectroscopic notation) with Ln=Pr, Nd, Er, Tm, and Yb, have been determined semiempirically from the dependence between calculated or empirical expectation values 〈r−3〉4f〈r−3〉4f and spin–orbit radial integrals ζ4f known from experimental free-ion spectra. The variation with 〈r−3〉4f〈r−3〉4f of the matrix elements of spin–orbit interactions for the ground levels of the same free ions has been also discussed.