Perturbation Energies for the Hooke's Law Model of the Two-Electron Atom

The Rayleigh–Schrödlinger perturbation energies $E^{\mathrm{(n)}}$ for the ground state of the Hooke's law model atom are calculated through tenth order. The $E^{\mathrm{(n)}}$ are expressed as singly infinite sums whose terms are obtained from recurrence relations. Very slow convergence limited the method to $E^{\text{(10)}}$ and below. The results are compared with those of Midtdal (1965) for heliumlike atoms, and it appears that the convergence of the Hooke series is more rapid. However, no recognizable patterns are observable in the Hooke $E^{\mathrm{(n)}}$ through $E^{\text{(10)}}$ . The nature and position of the singularity determining the radius of convergence is discussed.