DIMENSIONAL PERTURBATION-THEORY FOR EXCITED-STATES OF 2-ELECTRON ATOMS

Large-order dimensional perturbation theory, which yields high accurac y for ground-state energies, is applied here to excited states of the two-electron atom. Expansion coefficients are computed recursively usi ng the moment method, which we formulate in terms of normal coordinate s. We consider the first two excited S states of helium, corresponding , at the large-dimension limit, to one quantum in either the antisymme tric-stretch normal mode or the symmetric-stretch normal mode. Compari son with the hydrogenic limit has identified these states as Is 2s 3S and 1s2s 1S, respectively. We sum the 1/D expansions at D = 3, using s ummation procedures that take into account the dimensional singularity structure of the eigenvalues, and find convergence at D = 3 to the ei genvalues predicted by the hydrogenic assignments, despite apparent qu alitative differences between the eigenfunctions at large D and those at D = 3. In the D --> infinity limit, the electrons are equidistant f rom the nucleus. Our results for 1s2s energies appear to imply that th e shell structure is properly accounted for by terms in the expansion beyond the lowest order. This robustness of the 1/D expansion suggests that the method will be applicable to many-electron systems.