Parametrization of free ion levels of four isoelectronic 4f2 systems: Insights into configuration interaction parameters

The experimental free ion 4f2 energy level data sets comprising 12 or 13 J-multiplets of La+, Ce2+, Pr3+ and Nd4+ have been fitted by a semiempirical atomic Hamiltonian comprising 8, 10, or 12 freely-varying parameters. The root mean square errors were 16.1, 1.3, 0.3 and 0.3 cm−1, respectively for fits with 10 parameters. The fitted inter-electronic repulsion and magnetic parameters vary linearly with ionic charge, i, but better linear fits are obtained with (4−i)2, although the reason is unclear at present. The two-body configuration interaction parameters α and β exhibit a linear relation with [ΔE(bc)]−1, where ΔE(bc) is the energy difference between the 4f2 barycentre and that of the interacting configuration, namely 4f6p for La+, Ce2+, and Pr3+, and 5p54f3 for Nd4+. The linear fit provides the rationale for the negative value of α for the case of La+, where the interacting configuration is located below 4f2.