On the Z-expansion of atomic properties

The expansion of the wave function of S-2 atom in the presence of a scaled electric fietd epsilon' cannot be expanded simultaneously in lambda = Z(-1). where Z is the nuclear charge. and epsilon'. The fact that lambda cannot be used as an order parameter, equivalent to the breakdown of the usual perturbation theory expansion. is due to a degeneracy in the spectrum of H-0. This necessitates the partial summation of higher-order formal perturbation theoretic terms in order to remove an infinity in the leading term. The summation technique should be useful in other calculations on degenerate systems.