Asymptotic quantum defect of singly excited two-electron atoms at the critical charge

The validity of a conjecture concerning the asymptotic behavior of a singly-occupied atomic orbital of type nl outside an N-electron core, upon approaching the critical charge (below which this electron is not bound), is definitively demonstrated. According to this conjecture, this orbital becomes an infinitely diffuse hydrogenic orbital of type (n - n(l))l, where n(l) is the number of occupied (or partially occupied) core subshells with angular momentum l. An indicator of this asymptotic behavior is the asymptotic value of the corresponding quantum defect lim(Z -> N) delta(nl) = n(l). To establish this limiting behavior for several singly-excited states of the two-electron atom, we apply the explicitly correlated Hylleraas-type variational exponential expansion to evaluate highly precise energies, that allow the critical charge (Z(c) = 1) to be approached much more closely than ever before. The results suggest a refinement of the asymptotic form of the quantum defects in the various states considered, exhibiting the distinct origins of s-p splitting versus singlet-triplet splitting.