Mean-field calculations with regularized pseudopotentials
Résumé
Over the past decades, the Energy Density Functional (EDF) method has proven to be a tool of choice for the study of the entire chart of nuclei except the lightest ones. With the use of an effective interaction, a relatively simple ansatz for the wave function and the application of a variational principle, this method allows to account for a large set of properties of atomic nuclei such as their binding energies and shapes in their ground states, the energy levels of their rotational bands or their possible fission barriers. Most of the effective interactions found in the literature contain a density-dependent term. This term is used because it is known that an effective interaction only containing two-body density-independent terms can not satisfactorily reproduce the properties of nuclei and infinite matter at the mean-field level. Using a two-body density dependent term is a simple and very efficient way to cop with this problem. It is known that beyond-mean-field calculations such as the Generator Coordinate Method (GCM) or symmetry restorations can only be implemented with EDFs which are strictly derived from an interaction. But even with this constraint, it has been shown that the use of density-dependent terms leads to formal and technical problems for calculations beyond the mean-field approximation. In order to have an interaction usable at the mean-field level and beyond, without facing such difficulties, we developed an interaction written as a sum of so-called “regularized finite-range pseudopotentials”. In this approach, the EDF stems from a momentum expansion around a finite-range regulator (usually chosen as a Gaussian form factor) and thus have a form compatible with powerful effective-theory methods. The regularized two-body part of this interaction is complemented with a semi-regularized three-body term, i.e. a product of a Gaussian form factor multiplied with a Dirac delta-function. Recently, such a regularized interaction was adjusted and tested with mean-field calculations for infinite nuclear matter and spherical nuclei. The results are very promising a represent a proof of concept that this approach is valid and may be used in beyond-mean-field calculations.
