Eur. Phys. J. A (2021) 57: 151
https://doi.org/10.1140/epja/s10050-021-00458-z

Regular Article –Theoretical Physics

In-medium k-body reduction of n-body operators

A flexible symmetry-conserving approach based on the sole one-body density matrix

¹ IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
² Department of Physics and Astronomy, Instituut voor Kern-en Stralingsfysica, KU Leuven, 3001, Leuven, Belgium
³ Departamento de Física Teórica, Universidad Autónoma de Madrid, 28049, Madrid, Spain
⁴ CEA, DAM, DIF, 91297, Arpajon, France
⁵ Laboratoire Matière en Conditions Extrêmes, CEA, Université Paris-Saclay, 91680, Bruyères-le-Châtel, France

^a mikael.frosini.2014@polytechnique.org

Received: 21 February 2021
Accepted: 6 April 2021
Published online: 27 April 2021

Abstract

The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending their reach beyond mid-mass nuclei. Consequently, state-of-the-art ab initio calculations are typically performed while approximating three-nucleon interactions in terms of effective, i.e. system-dependent, zero-, one- and two-nucleon operators. While straightforward in doubly closed-shell nuclei, existing approximation methods based on normal-ordering techniques involve either two- and three-body density matrices or a symmetry-breaking one-body density matrix in open-shell systems. In order to avoid such complications, a simple, flexible, universal and accurate approximation technique involving the convolution of the initial operator with a sole symmetry-invariant one-body matrix is presently formulated and tested numerically. Employed with a low-resolution Hamiltonian, the novel approximation method is shown to induce errors below $2-3\%$ across a large range of nuclei, observables and many-body methods.