Brueckner self-consistent calculations are performed for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nuclei with various modern hard-core interactions. Elements of the $G$ matrix are calculated by the reference-spectrum method, while $Q-1\mathrm{}$ corrections are made by matrix inversion in the proper single-particle space. Thus, it is not assumed that $Q$ commutes with the center-of-mass motion. The prescription for selecting the appropriate spectrum of single-particle excited states is investigated by comparing results of the Brueckner method with other calculations. These comparisons indicate that the particle spectrum should be left unperturbed. One then finds that the Hamada-Johnston, Yale, and Reid (hard-core) interactions yield about one half the binding energy of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The calculated results are dissected into shell-model components. This analysis indicates that the short-range part of the hard-core interaction is too strongly repulsive.

• Received 30 August 1971

DOI:https://doi.org/10.1103/PhysRevC.6.101