The reliability of various approximation procedures has been investigated for the low-lying $J^{\pi }=3^{-}$, $T=0\mathrm{}$ state in ${\mathrm{O}}^{16}$ and the associated ground-state correlations. To see the effects of emphasizing or suppressing the octupole correlations, we have used a conventional shell-model Hamiltonian but added (or subtracted) various amounts of an octupole-octupole interaction. Comparison with an exact diagonalization, within the limited model space, shows that the equations of motion, in the particle-hole approximation, give excellent results in the vibrational region of small octupole correlations. The results are much better than those of the random-phase approximation, which ignores the Pauli blocking effects of ground-state correlations. The procedure of variation of a deformed intrinsic determinant after angular momentum projection is found to be excellent in the rotational region of large octupole correlations. But already in the vibrational region, it is at least as good as the random-phase approximation, and would be even better if a more general intrinsic determinant were allowed. Both the equations-of-motion and the projection method give reasonable results in the transition region.

• Received 25 July 1969

DOI:https://doi.org/10.1103/PhysRev.188.1640