Unitary-Model-Operator Approach to Nuclear-Structure Physics. II. Applications

Results are reported for Hartree-Fock calculations carried out with an effective interaction derived from the Yale potential. The spherical nuclei ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$ are considered. The orbitals are expanded in terms of harmonic-oscillator functions, and the dependence of the results on the number of oscillator functions used and upon the oscillator size parameter is studied. The importance of various second-order terms is considered using a simple approximation for the Pauli operator and the energy denominators. For the second-order terms in the tensor interaction, some spectral corrections to the simplified energy denominators are made. Reasonable results are obtained for the nuclei considered; however, the spectral corrections to the simplified energy denominators are found to provide an important correction to the calculated binding energy. It is concluded that an improved treatment of the energy denominators is required to improve the accuracy of the results reported here. Tables of the effective interaction used in these calculations are presented in an Appendix.