Hartree-Fock approximation for the<i>ab initio</i>no-core shell model

Abstract

The spherical Hartree-Fock approximation is applied to the ab initio no-core shell model, with a realistic effective nucleon-nucleon interaction in order to investigate the range of its utility. Hartree-Fock results for binding energies, one-body density distributions, and occupation probabilities are compared with results from exact diagonalization in similar model spaces. We show that this mean-field approximation, especially with second-order corrections, is able to provide some useful approximations for $^{4}\mathrm{He}$ and $^{16}\mathrm{O}$. We also explore the physical insights provided by the Hartree-Fock results for single-particle properties such as spin-orbit splittings. We find single-particle state ordering consistent with the phenomenological shell model.