Atomic many-body perturbation theory using radially restricted basis functions

Abstract

The construction of a potential barrier around an atom such that a chosen zeroth-order reference state is left unaffected results in a square-integrable virtual basis set with rapid convergence properties for use in atomic many-body perturbation theory. Encouraging results have been obtained using this technique for calculations of the correlation energies and transition probabilities of small atoms and ions. In the case of ${\mathrm{H}}^{-}$ it is shown that the conventional formulation of many-body perturbation theory involving continuum functions produces classes of energy diagrams which diverge with order, although the total summation remains finite. No such divergence is present in a properly constructed contracted basis set.