Molecular-orbital description of doubly excited atomic states generalized to arbitrary dimension.

Abstract

The molecular-orbital description of two-electron atoms [J. M. Feagin and J. S. Briggs, Phys. Rev. A 37, 4599 (1988)], derived from ${\mathrm{H}}_{2}^{+}$ by interchanging the roles of electrons and nuclei, is generalized to D dimensions. For ${\mathrm{H}}_{2}^{+}$ itself there exist myriad exact interdimensional degeneracies because D\ensuremath{\rightarrow}D+2 is equivalent to m\ensuremath{\rightarrow}m+1, augmenting by unity the projection of the electronic angular momentum on the internuclear axis. When the molecular orbitals (MO's) are transcribed to treat two-electron motion, additional constraints limit the exact degeneracies to states in D=3 and 5, but many approximate degeneracies persist. Since the MO description emphasizes rotational properties of the two-electron atom, the link between dimension and orbital angular momentum is a pervasive feature. We use this link to classify groups of quasidegenerate doubly excited atomic energies and to explain striking similarities among certain pairs of hyperspherical or molecular-orbital two-electron potential curves.