arXiv:nucl-th/0312008v1 2 Dec 2003 Hartree-Fock Approximation for the Ab Initio No-Core Shell Model Mahmoud A. Hasan 1 , James P. Vary 2 and Petr Navr´atil 3 (1) Department of Physics, Applied Science University Amman, Jordan (2) Department of Physics and Astronomy, Iowa State University Ames, Iowa 50011 (3) Lawrence Livermore National laboratory, Livermore, California 94550 December 18, 2013 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 proba- bilities 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 approxima- tons for 4 He and 16 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 phe- nomenological shell model. 1 Introduction Recently, the ab initio no-core shell model (NCSM) has been applied with re- alistic effective nucleon-nucleon (NN) interactions to light nuclei up to A=12 [1, 2, 3, 4]. With the need to extend to heavier systems and to incorporate improvements such as effective and real three-body forces in ever larger model spaces, the prospect for near-term results is limited by present day compu- tational resources. In light of this situation, there is a need for approximate methods to extend the ab initio NCSM to heavier systems with a wide range of observables to compare with experiment. Hartree-Fock is a proven tool for semi-realistic interactions for even the heav- iest of nuclei [5] and is sufficiently flexible to handle many-body forces through 1