Kinetic-energy operator in the effective shell-model interaction

Abstract

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.