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−1 perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The Z−1 expansion of the correlation energy is compared with that for heliumlike atoms and found to be similar.