Goldstone-Brueckner perturbation theory extended in terms of mixed nonorthogonal Slater determinants

Abstract

The Goldstone-Brueckner perturbation theory is extended to incorporate in a simple way correlations associated with large amplitude collective motions in nuclei. The new energy expansion making use of non-orthogonal vacua still allows to remove the divergences originating from the hard-core of the bare interaction. This is done through the definition of a new Brueckner matrix summing generalized Brueckner ladders. At the lowest-order, this formalism motivates variational calculations beyond the mean-field such as the Generator Coordinate Method (GCM) and the Projected Mean-Field Method from a perturbative point of view for the first time. Going to higher orders amounts to incorporate diabatic effects in the GCM and to extend the projection technique from product states to well-defined correlated states.The mean-field approximation relies on a particular choice of the approximate trial-state of the system, namely a Slater-determinant | Φ α 0 [1] * describing the system as N independent particles. The mean-field approximation can also be viewed as the zero-order approximation of the actual ground-state energy in a perturbative expansion written in terms of the residual interaction.In the case of nuclear structure, the mean-field approximation fails from the outset because of the strong repulsive core of the bare nucleon-nucleon interaction which leads to divergences when limiting the perturbative expansion to any order in the interaction. However, Brueckner [2] showed that the energy expansion can be reordered as a function of hole-lines number in the graphs, which amounts to an expansion in the density of the system. Such a reordering takes care of two-body short-range correlations induced by the repulsive core of the nucleon-nucleon interaction. It leads to an expression of the energy in terms of a renormalized interaction G. Using it, one can study the lowest-order approximation and define a meaningful mean-field picture.One can then evaluate the improvements achieved by including higher order diagrams since each of them is well-behaved.In many-body systems, several ways to go beyond the mean-field approximation exist, depending upon the physical situation of interest [1]. Without particularly relating it to any perturbative expansion, one can improve the approximate trial wave-function of the system in a variational picture * In its generalized form taking care of static pairing correlations, the mean-field approximation makes use of a state being a product of independent quasi-particles instead of independent particles.

Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes

“…In principle, they should be readjusted, at least to account for the extra binding energies due to rotational and vibrational correlations. Furthermore, our results could be affected by considering other generalizations of the density dependence of the Skyrme force when calculating non-diagonal matrix elements, as suggested by Duguet and Bonche [53,54]. Such an investigation is presently underway.…”

Nuclear response for the Skyrme effective interaction with zero-range tensor terms

“…The number of parameters becoming larger, it is of particular importance to define a clever fitting strategy. Acceptable ranges of variation for the parameters can be motivated by linking the Skyrme EDF to realistic interactions using many-body perturbation theory on top of renormalized low momentum interactions [28,29]. It is also obviously mandatory to locate the regions in parameters space that lead to instabilities.…”

Simple regularization scheme for multireference density functional theories

“…These include hermiticity, independence of scalar observables on the orientation of the intrinsic system, and consistency with the underlying mean field. The alternative way of proceeding is to substitute density-dependent terms with projected density [14] or average density [15]. These scenarios do not fulfill the consistency criteria and will not be discussed here.…”