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Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

  • Regular Article –Theoretical Physics
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Abstract

Large-scale models of nuclear structure are currently the only way to provide consistent datasets for the many properties of thousands of exotic nuclei that are required by nucleosynthesis simulations. In [W. Ryssens et al., Eur. Phys. J. A 58, 246 (2022)], we recently presented the new BSkG2 model based on an energy density functional of the Skyrme type. Relying on a flexible three-dimensional coordinate representation of the nucleus, the model takes into account both triaxial deformation and time-reversal symmetry breaking. BSkG2 achieves a state-of-the-art global description of nuclear ground state (g.s.) properties and reproduces in particular the known masses with a root-mean-square (rms) deviation of 678 keV. Moving beyond g.s. properties, the model also reproduces all empirical values for the primary and secondary barriers as well as isomer excitation energies of actinide nuclei with rms deviations below 500 keV, i.e. with unprecedented accuracy. Here we discuss in detail the extension of our framework to the calculation of the fission barriers of 45 actinide nuclei, including odd-mass and odd-odd systems. We focus in particular on the impact of symmetry breaking which is key to the accuracy of the model: we allow systematically for axial, reflection and time-reversal symmetry breaking. The effect of the latter on the fission properties of odd-mass and odd-odd nuclei is small, but we find that allowing for shapes with triaxial or octupole deformation, as well as shapes with both, is crucial to achieving this accuracy. The numerical accuracy of our coordinate space approach, the variety of nuclear configurations explored and the simultaneous successful description of fission properties and known masses makes BSkG2 the tool of choice for the large-scale study of nuclear structure.

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Data Availability Statement

The manuscript has data included as electronic supplementary material.

Notes

  1. For microscopic-macroscopic models an accurate description of fission barriers deteriorates the description of the masses, hence why Ref. [6] advocates using two separate models: FRDM for masses and FRLDM for fission.

  2. As for the g.s. calculations of Ref. [12], we still impose z-signature as self-consistent symmetry which implies that \(\beta _{\ell m}\) vanishes if m is odd.

  3. We note that the tables of Ref. [88] and [89] report on deformation parameters that characterize the surface of the nuclear shape. These are not equal to our \(\beta _{\ell m,c}\), which characterize the shape of the nuclear volume, see the discussion in Refs. [87, 90] and references therein. For this reason, the experimental values for the \(\beta _{\ell m,c}\) quoted in the text are charge multipole deformations that we consistently calculated from the electric transition moments [91] that are also provided by these references.

  4. The total energy, on which the construction of the LEP is based, is a smooth function as seen on the top panel of Fig. 3. Its decomposition is not: the discrete steps in \(\beta _{22}\) of the LEP are visible in the non-smooth parts of the LEP curves in Fig. 5.

  5. Ref. [67] lists in fact 30 isomer excitation energies, but we drop for simplicity the values for \(^{235}\)Pu and \(^{244}\)Bk for which RIPL-3 lists no empirical barriers.

  6. An increase of the rotational correction lowers the outer barrier more than the inner barrier, see the discussion around Fig. 5. For the heavier nuclei, the inner one tends to be the primary barrier such that an increase of b implies a larger difference between primary and secondary barriers. For the lighter nuclei, the opposite happens.

  7. We also note that both models were constructed with rather different numerical schemes: BSk14 relied on an expansion in a limited number of harmonic oscillator shells while we rely here on a coordinate space representation.

  8. Other sets of fission data obtained with SkM* exist, such as Ref. [82], but Ref.  [73] reports the most extensive data set that we are aware of.

  9. Only the Coulomb energy and surface energy require the numerical evaluation of an integral. Nevertheless, the numerical accuracy of these terms should be easily controllable [6].

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Acknowledgements

We would like to thank A. Afanasjev, S. Giuliani and P.-G. Reinhard for providing us with additional data on their calculations for use in Sect. 4.4.: these concern Refs. [106, 111, 112], respectively. We also thank J.-F. Lemaître for sharing his flooding code. W.R. acknowledges useful discussions with N. Schunck. This work was supported by the Fonds de la Recherche Scientifique (F.R.S.-FNRS) and the Fonds Wetenschappelijk Onderzoek-Vlaanderen (FWO) under the EOS Project nr O022818F. The present research benefited from computational resources made available on the Tier-1 supercomputer of the Fédération Wallonie–Bruxelles, infrastructure funded by the Walloon Region under the grant agreement nr 1117545. The funding for G.S. from the US DOE, Office of Science, Grant No. DE-FG02-97ER41014 is greatly appreciated. S.G. and W.R. acknowledge financial support from the F.R.S.-FNRS (Belgium). Work by M.B. has been supported by the French Agence Nationale de la Recherche under grant No. 19-CE31-0015-01 (NEWFUN).

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  1. Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, Campus de la Plaine CP 226, Brussels, 1050, Belgium

    Wouter Ryssens, Guillaume Scamps & Stephane Goriely

  2. Department of Physics, University of Washington, Seattle, Washington, 98195–1560, USA

    Guillaume Scamps

  3. Université de Lyon, Université Claude Bernard Lyon 1, CNRS / IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, 69622, France

    Michael Bender

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Correspondence to Wouter Ryssens.

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Ryssens, W., Scamps, G., Goriely, S. et al. Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2. Eur. Phys. J. A 59, 96 (2023). https://doi.org/10.1140/epja/s10050-023-01002-x

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