SO leads to errors larger than +100%, while the SOC mean field Hamiltonian, both within and without the atomic approximation, shows errors similar to those affecting Eu 3+ atom (µ ≈ +5%), with small standard deviations (systematic errors) whereas the size of the statistical sample is not too small, that is, for the 7 F J levels with J > 1. It is noteworthy that H ABP SO accurately reproduces the true Breit-Pauli results for all the excited multiplets.