Correlations in nuclei. Self-consistent treatment and the BAGEL approach☆

Abstract An approach is presented which allows a self-consistent description of the fragmentation of single-particle strength for nucleons in finite nuclei employing the Green function formalism. The self-energy to be considered in the Dyson equation for the single-particle Green function contains all terms of first (Hartree-Fock) and second order in the residual interaction. It is demonstrated that the fragmentation of the single-particle strength originating from the terms of second order can efficiently be described in terms of the so-called BAGEL approximation. Employing this approximation the self-energy can be evaluated in a self-consistent way, i.e. the correlations contained in the Green function are taken into account for the evaluation of the self-energy. As an example this scheme is applied to the nucleus 16 O, using a realistic nucleon nucleon interaction. The effects of the correlations on the occupation probabilities and the binding energy are evaluated.