Hylleraasndash;Pekeris treatment ofDhyphen;dimensional twohyphen;electron atoms

摘要

The algorithm of Pekeris forSstates of twohyphen;electron atoms is generalized to spaces of arbitrary dimensionality. Numerical calculations are reported for the ground state (1thinsp;1S) and first two excited states (2thinsp;3Sand 2thinsp;1S) for a wide range of dimensions, 1Dinfin;, and nuclear charge, 1le;Zle;6. The accuracy is typically better than one part in 108. The energy eigenvalues may be continued to arbitrary real values of the parameter dgr;=1/D. Real atoms, withD=3, connect smoothly with simple, exactly known limits atDrarr;1 andDrarr;infin;. Analysis of the data permits several further terms in the 1/Dexpansion for the ground state energy to be determined, up to orderDminus;12. This indicates that the expansion does not converge forD=3 but terms of third to sixth order do conform approximately to a geometric series form, as previously postulated in order to carry out dimensional interpolation. The excited state data exemplify near continuum motion atDrarr;1 and quasivibrational asymmetric and symmetric stretching modes of electron motion asDrarr;infin;.