https://doi.org/10.1140/epja/s10050-025-01596-4
Regular Article - Theoretical Physics
Mean-field approximation on steroids: exact description of the deuteron
1
ESNT, IRFU, CEA, 91191, Gif-sur-Yvette, France
2
IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
3
CEA, DAM, DIF, 91297, Arpajon, France
4
Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680, Bruyères-le-Châtel, France
5
KU Leuven, Department of Physics and Astronomy, Instituut voor Kern- en Stralingsfysica, 3001, Leuven, Belgium
Received:
4
October
2024
Accepted:
14
May
2025
Published online:
18
June
2025
The present article demonstrates that the deuteron, i.e. the lightest bound nuclear system made of a single proton and a single neutron, can be accurately described within a mean-field-based framework. Although paradoxical at first glance, the deuteron ground-state binding energy, magnetic dipole moment, electric quadrupole moment and root-mean-square proton radius are indeed reproduced with sub-percent accuracy via a low-dimensional linear combination of non-orthogonal Bogoliubov states, i.e. with a method whose numerical cost scales as 
, where 
is the dimension of the basis of the one-body Hilbert space. By further putting the system into a harmonic trap, the neutron-proton scattering length and effective range in the 
channel are also accurately reproduced. To achieve this task, (i) the inclusion of proton-neutron pairing through the mixing of proton and neutron single-particle states in the Bogoliubov transformation and (ii) the restoration of proton and neutron numbers before variation are shown to be mandatory ingredients. This unexpected result has implications regarding the most efficient way to capture necessary correlations as a function of nuclear mass and regarding the possibility to ensure order-by-order renormalizability of many-body calculations based on chiral or pionless effective field theories beyond light nuclei. In this context, the present study will be extended to 
H and 
He in the near future as well as to the leading order of pionless effective field theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
