Mean-field calculations with regularized pseudopotentials

Karim Bennaceur (Université Claude Bernard Lyon 1, CNRS/IN2P3 IP2I, France)

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 [1].

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 [2,3]. 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 [4]. 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 [5,6].

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” [7,8]. 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.


[1] M. Bender, P.H. Heenen, P.G. Reinhard, Rev. Mod. Phys. 75 (2003) 121.
[2] V.F. Weisskopf, Nucl. Phys. 3, 423 (1957).
[3] D. Davesne, J. Navarro, J. Meyer, K. Bennaceur and A. Pastore, Phys. Rev. C 97, 044304 (2018).
[4] M. Anguiano, J.L. Egido, L.M. Robledo, Nucl. Phys. A696 (2001) 467.
[5] L M Robledo, J. Phys. G: Nucl. Part. Phys. 37 (2010) 064020.
[6] T. Duguet, M. Bender, K. Bennaceur, D. Lacroix, T. Lesinski, Phys. Rev. C79, 044320 (2009).
[7] J. Dobaczewski, K. Bennaceur, F. Raimondi, J. Phys. G: Nucl. Part. Phys. 39 (2012) 125103.
[8] K. Bennaceur, A. Idini, J. Dobaczewski, P. Dobaczewski, M. Kortelainen
and F. Raimondi, J. Phys. G: Nucl. Part. Phys. 44 (2017) 045106.