Comparison of various approximations for the ground state of ¹⁶O

The amount and nature of 2 particle-2 hole correlations in the ground state of ¹⁶O was investigated using various approximations. First 2h{stroke}ω excitations were considered with the particles in the 2s-1d shell and the holes in the 1p shell. Matrix diagonalization, with spurious states removed, resulted in 22% 2p-2h ground state correlations and a depression of the ground state energy of 7.9 MeV; if spurious states were incorrectly included, then both numbers were nearly doubled. The corresponding numbers for the RPA were 43% and 8.2 MeV using the quasi-boson approximation. This approximation is suggested to be inaccurate. Ordinary perturbation theory gave results remarkably close to matrix diagonalization. The corresponding wave functions had an overlap of .993. The correlations were spread over very many j-j coupling states but could be localized to relatively few states in the L-S representation. Perturbation theory was used in a larger space where the 2 particle-2 hole energy could be greater than 2h{stroke}ω. This led to 32% 2p-2h correlations and the ground state depression was 24 MeV. The correlations with 2h{stroke}ω and 4h{stroke}ω energy were comparable. A dispersion method gave less correlation but qualitatively similar results. In the smaller configuration space the first excited 0⁺ state was at 24 MeV excitation energy relative to the ground state, but a more realistic estimate is probably about 14 MeV. This state looked slightly simpler in j-j rather than L-S coupling.