New analyses of energy level datasets for LaCl₃: Ln³⁺ (Ln = Pr, Nd, Er)

The electron spin–spin interaction (Hss) has long been omitted by many previous researchers in the empirical study of lanthanide spectroscopic data in the last four decades. In this work, the corresponding operator is specifically included into the semi-empirical Hamiltonian for 4fᴺ tripositive lanthanide ions and its consequences are investigated by fitting the experimental energy level data available for LaCl₃ doped with Pr³⁺, Nd³⁺ and Er³⁺, taking into account polarization and Zeeman studies. The inclusion does not require additional parameters. For these systems, respectively: 61, 127, 83 experimental crystal field levels were fitted by 14, 20, 20 parameters, giving root mean square (r.m.s.) errors (in cm⁻¹) of 6.4, 8.1, 7.0. These errors are significantly smaller than those for best-fit calculations where Hss is omitted. With the exception of calculations by Crosswhite et al. for Pr³⁺ and Nd³⁺, the results of our present fits are significantly different from those of many previous researchers, probably attributed to errors or improper use of the reduced matrix elements for various free-ion operators. The inclusion of Hss into the energy level calculation can change state energies by almost three times the overall calculation r.m.s. error, and the changes vary considerably from one multiplet term to another. The spin–spin interaction has an effect upon the J-mixing between different multiplets and the impact can be appreciable in some cases, especially for dealing with the correlation crystal field. Since all the two body interaction operators are non-orthogonal within the 4fᴺ configuration, their corresponding free-ion parameters are correlated with each other, depending upon the set of energy levels chosen in the fit. Hence, there is much doubt about the reliability of parameter values as derived from previous studies which are quite different from those of our present study. Copyright © 2013 Elsevier B.V. All rights reserved.