Je. Hansen et al., INTERPRETATION OF HIGHER-ORDER MAGNETIC EFFECTS IN THE SPECTRA OF TRANSITION-METAL IONS IN TERMS OF SO(5) AND SP(10), Physical review letters, 78(16), 1997, pp. 3078-3081
Small discrepancies in the fitted energy levels of the configurations
3d(N) of transition metal ions are ascribed to effective three-electro
n magnetic operators y(i). Surprisingly it has been found that, of the
16 possible operators with ranks 1 in both spin and orbital spaces, f
our operators labeled by the irreducible representation (irrep) (11) o
f SO(5) are sufficient to obtain results which appear to be limited by
the errors in the experimental energy levels. An interpretation is gi
ven involving products of operators labeled by the irreps of SO(5) and
the symplectic group Sp(10).