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Moving away from singly-magic nuclei with Gorkov Green’s function theory

  • Regular Article –Theoretical Physics
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Abstract

Ab initio calculations of bulk nuclear properties (ground-state energies, root-mean-square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green’s function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, \(NN\)+\(3N\text {(lnl)}\) and NNLO\(_{\text {sat}}\). An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers \(N=28,32,34\) emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlations in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical work and no experimental data were generated. Data associated to the theoretical simulations can be obtained from the authors upon request.]

Notes

  1. This automatically imposes the same restriction on the \(e_{2\text {max}}\) at play in three-body operators, for which then \(\left( e^{3\text {-body}}_{1\text {max}}, e^{3\text {-body}}_{2\text {max}}, e^{3\text {-body}}_{3\text {max}}\right) = (13, 16, 16)\).

  2. A notable exception is represented by energy differences near a closed shell, where errors related to the breaking of particle-number do not cancel between a closed-shell and and open-shell system.

  3. Present calculations could not be extended beyond \(N=40\) due to convergence issues, see discussion in Ref. [8] for more details.

  4. For potassium only \(S_\text {1p}\) can be computed, while for argon none of the two separation energies is available in the present calculations.

  5. Experimentally, the dripline is typically established by means of a void observation of one or several isotopes rather than by determining a negative value of \(S_\text {1p}\) or \(S_\text {2p}\).

  6. Note that \(\varDelta ^{(3)}\) corresponds to half of the energy difference between the lowest unoccupied quasiparticle and the highest occupied quasihole states, that is the particle-hole neutron gap at the Fermi surface. At subshell closures, this is dominated by the gap among different nuclear orbits. However, for open neutron shells only the pairing contribution remains.

  7. Only charge radii of bound isotopes are shown in the following, i.e. in Figs. 11, 12 and 13. While all computed argon and calcium nuclei are found to be bound, titanium and chromium isotopes with \(N=14,16,18\) result unbound in the present calculations (with both \(NN\)+\(3N\text {(lnl)}\) and NNLO\(_{\text {sat}}\) interactions).

  8. Notice that this differentiation also applies to odd-Z chains around calcium and extends up to iron, see Ref. [80].

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Acknowledgements

The authors wish to thank M. Frosini for providing the particle-number projected HFB results discussed in Sect. 2, as well as R. Garcia Ruiz and F. Raimondi for useful exchanges. Calculations were performed by using HPC resources from GENCI-TGCC (Contracts no. A005057392, A007057392) and at the DiRAC Complexity system at the University of Leicester (BIS National E-infrastructure capital Grant no. ST/K000373/1 and STFC Grant no. ST/K0003259/1). This work was supported by the United Kingdom Science and Technology Facilities Council (STFC) under Grant no. ST/L005816/1 and in part by the NSERC Grant no. SAPIN-2016-00033. TRIUMF receives federal funding via a contribution agreement with the National Research Council of Canada.

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Authors and Affiliations

  1. IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France

    V. Somà & T. Duguet

  2. Department of Physics, University of Surrey, Guildford, GU2 7XH, UK

    C. Barbieri

  3. Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133, Milano, Italy

    C. Barbieri

  4. INFN, Sezione di Milano, Via Celoria 16, 20133, Milano, Italy

    C. Barbieri

  5. KU Leuven, Institut voor Kern-en Stralingsfysica, 3001, Leuven, Belgium

    T. Duguet

  6. TRIUMF, 4004 Westbrook Mall, Vancouver, BC, V6T 2A3, Canada

    P. Navrátil

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  1. V. Somà
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  2. C. Barbieri
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Correspondence to V. Somà.

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Communicated by Jerome Margueron.

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Somà, V., Barbieri, C., Duguet, T. et al. Moving away from singly-magic nuclei with Gorkov Green’s function theory. Eur. Phys. J. A 57, 135 (2021). https://doi.org/10.1140/epja/s10050-021-00437-4

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