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

The Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar $Z^{\text{−1}}$ perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The $Z^{\text{−1}}$ expansion of the correlation energy is compared with that for heliumlike atoms and found to be similar.