Nonsymmetric Perturbation Calculations of Excited States of Helium

Abstract

Perturbation-theoretic calculations are carried out for the lowest five states of the helium atom using a Hamiltonian which is not symmetric in the particle indices such that the zerothorder spatial functions can be written as simple products of hydrogenic orbitals. The perturbation expansions are reasonably convergent except for the fifth state which is divergent as expected. By 19th order in the expansion the energies of the first two excited states are accurate to 2 × ${10}^{-4\mathrm{}}$ and the expectation values of $\frac{1}{2}(1\mathrm{}\pm P)$ are accurate to 1 × ${10}^{-4\mathrm{}}$.