Variable dimensionality in the group-theoretic prediction of configuration mixings for doubly-excited helium

Variable dimensionality (= D) is used to interpret recent group-theoretic predictions of configuration mixings in doubly-excited helium. Calculated 2s2:2p2 1S mixings agree with the group theory over the range 1 ⩽ D ⩽ ∞. General results for D = 2 predicted mixings are given and energies of states within the N = 2 atomic shell confirm predicted level orderings. The D = 1 model atom is described exactly by the group theory, with quantum numbers and a selection rule characterizing the stability of Coulomb matrix elements as D → 1. The exact D = 1 results have a physical interpretation in approximate autoionization and energy selection rules for Rydberg series at D = 3.