Channel invariants and SU(3) classification for two-electron atoms

Abstract

Previous studies showed the configuration-mixed excitation channel structure of two-electron atoms to be classified by two quantum numbers $K$ and $T$. Three new aspects of the classification are considered here: (i) $K$ and $T$ are shown to be limiting cases of two exact invariants for channels in the asymptotic regime ${r}_{2}\ensuremath{\gg}{r}_{1}$. The invariants classify channels for the entire isoelectronic series. Sum rules, quantum number correlation diagrams for isoelectronic series, and perturbation formulas for the invariants are described. (ii) The $K$, $T$ spectrum is shown to be contained in a chain SU(4) \ensuremath{\supset} SU(3) \ensuremath{\supset} SU(2) defined mathematically on the two-electron channels. Possible physical connection with O(6) quantum numbers for noninteracting particles in hyperspherical coordinates is discussed. (iii) An empirical link is established between autoionization stability of heliumlike atoms, and unitarity of irreducible representations for a SU(2, 1) channel scheme. The noncompact classification also includes channels for double ionization.