Investigation of the States of2s−1dShell Nuclei Based on the Four-Particle-Four-Hole State inO16

The four-particle-four-hole state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and the corresponding states in the even-even, $N=Z$ nuclei of the $2s-1d$ shell have been investigated in the framework of the Hartree-Fock approximation. Detailed calculations were performed in each case to determine the most stable Hartree-Fock solution. By assuming a simple model, the excitation energies of the band heads were calculated showing that ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ is the last nucleus where a state analogous to the four-particle-four-hole state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ might be observed. Energy levels have been calculated in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ using a basis of good angular-momentum states. A comparison between the predicted and the observed energy spectrum has been shown. In ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, calculations have been performed both with phenomenological and realistic interactions and the results have been compared. The accuracy of the projected angular-momentum states from the twelve-particle-four-hole solution in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ has been estimated and shows that the projected states in this case are close to the eigenstates. We have demonstrated that one of two $0^{+}$ states observed around 7 MeV in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is an eight-particle-four-hole state.