Spin-orbit interaction in the first excited 4f-level in trivalent lanthanides

[Display omitted] •Original results are presented for free Ln IV ions and Ln3+: LaF3 crystals.•Matrix elements of spin–orbit interaction are found in the lowest two 4f levels.•The quantities are correlated with the populations and the number N in 4fN.•The concept of nephelauxetic effect in spin–orbit coupling constants is revised. The spin–orbit interaction has been considered for the first excited 4f- level in free ions Ln IV and Ln3+: LaF3 crystals. The matrix elements of spin–orbit interaction have been calculated and varied with the level population at T = 298.15 K. It has been found that the first excited 4f- levels in these systems exhibit lower values of matrix elements than those for the ground levels, except Yb IV, Yb3+: LaF3. The ratio of the spin–orbit coupling constants ζ4f (crystal)/ζ4f (free ion) is ≤1 in the series, thus revising the concept for nephelauxetic effect in this relation.