Phase Conspiracy in Unoccupied Hartree-Fock Orbitals

Second order energies and the probabilities of two-particle, two-hole components in the ground states of ${\mathrm{He}}^4$ and ${\mathrm{O}}^{16}$, calculated using perturbation theory in Hartree-Fock bases, show that excitations to high lying levels are more important than the shell model predicts. The importance of these excitations stems from the relative phases of the Hartree-Fock wave functions for unoccupied states and this phase relation can be explained quite simply.