Selection rules for some three-electron operators in the atomic f shell

Abstract

Of the six three-electron operators ti used in configuration-interaction studies involving f electrons, three (t6, t7 and t8) belong to the irreducible representation (420) of Racah's group SO(7). They are distinguished by the labels (22), (40), and (42) of the subgroup G2. The labels appropriate to the expanded group SO(8) are superpositions of (3311), (4220), (4310) and (4400). The sequence SO(8) to SO(7) to G2 is augmented by SO(8) to SO(7)' G2, where the generators of SO(7)' differ from those of SO(7) in that the creation and annihilation operators for f electrons are replaced by those appropriate to quark-like objects which also possess three units of angular momentum. Selection rules deriving from the irreducible representations of SO(7)' are interpreted in terms of the classic labelling scheme of Racah. This procedure leads to selection rules for the three ti near the comparatively inaccessible middle of the f shell, and it gives an explanation for many of the apparently accidental zeros found by sifting the computer output of Dr W T Carnall (1992).