Application of the reaction-matrix theory (II). Simple Brueckner-Hartree-Fock descriptions of the ground states of light nuclei

Abstract

The derivation of the nuclear single-particle (s.p.) shell model from realistic free-space nucleon-nucleon potentials is studied both theoretically and quantitatively. A Brueckner-Hartree-Fock (BHF) s.p. model is constructed which contains a reaction-matrix HF s.p. potential and a potential coming from other many-body correlations. The s.p. Hamiltonian is defined diagrammatically. The nature of the resulting s.p. states and the relation between the resulting s.p. energies and the corresponding energies in nuclear matter are elucidated. Particular attention is paid to the important third-order hole-hole re-arrangement potential, which is here calculated explicitly with finite geometry. This BHF model is then used to study quantitatively the ground-state properties of the light nuclei 40Ca, 16O and 4He using a number of hard-core nucleon-nucleon potentials, some with non-central forces. It is found that the calculation underbinds these light nuclei by 2–4 MeV per particle for realistic potentials but does give rough agreement in the nuclear radii except in 4He. The calculation does not give the correct s.p. removal energies, with or without the inclusion of the second- and third-order re-arrangement potentials. It also gives only half of the empirical spin-orbit splitting. It is further estimated that a realistic nucleon-nucleon potential giving the correct binding energy in nuclear matter will correctly bind these light nuclei if the contribution of long-range ground-state correlations is included. The nuclear size will also be roughly correct. Comparison between the present calculation and a number of other calculations in the literature is made in some detail.