Differences in the Hartree-Fock and effective shell-model interaction arising from alternative treatments of the kinetic-energy operator in finite nuclear many-body problems are described. The Hartree-Fock single-particle energies and their relationship to experimental removal energies depend sensitively on whether or not the center-of-mass kinetic energy is retained in the nuclear Hamiltonian. Large effects in particle-hole energies are obtained which have important consequences for effective shell-model Hamiltonians. If the center-of-mass contribution of the kinetic-energy operator is removed from the Hamiltonian, substantial effects appear in a simple example of the shell-model spectra of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ treated as four and five valence nucleons, respectively, outside a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core. The contributions to the energy coming from the valence, relative kinetic-energy operator push the energy spectra of both nuclei up by about 1 MeV relative to their ground states.

• Received 14 July 1992

DOI:https://doi.org/10.1103/PhysRevC.46.2333