The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full $0ħ\omega$ shell-model spaces we calculate the Hartree-Fock $\mathrm{}\left(\mathrm{HF}\right)\mathrm{}+\mathrm{RPA}$ binding energy, and compare it to exact diagonalization. We find that often, but not always, the $\mathrm{HF}+\mathrm{RPA}$ gives a good approximation to the “exact” ground state energy. In those cases where the RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wave function. This weakens the reliability of the RPA for computing binding energies.

• Received 20 May 2002

DOI:https://doi.org/10.1103/PhysRevC.66.034301