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Electromagnetic moments of ground and excited states calculated in heavy odd-N open-shell nuclei

J. Dobaczewski1,2, A. E. Stuchbery3, G. Danneaux4, A. Nagpal1, P. L. Sassarini1, and H. Wibowo1

  • 1School of Physics, Engineering and Technology, University of York, Heslington, York YO10 5DD, United Kingdom
  • 2Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
  • 3Department of Nuclear Physics and Accelerator Applications, Research School of Physics, Australian National University, Canberra ACT 2601, Australia
  • 4Department of Physics, University of Jyväskylä, PB 35(YFL) FIN-40014 Jyväskylä, Finland

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Phys. Rev. C 113, 024306 – Published 5 February, 2026

DOI: https://doi.org/10.1103/4q99-rv67

Abstract

Within nuclear density-functional theory, we calculated spectroscopic magnetic-dipole and electric-quadrupole moments for various quasiparticle configurations of odd-N, even-Z, 83≤N≤125 nuclei ranging from gadolinium to osmium. By tagging the blocked quasiparticles with single-particle states of the semimagic dysprosium isotope, we efficiently computed 22 prolate and 22 oblate states for each of the 154 nuclei and tracked them across the entire major neutron shell. We compared this extensive set of theoretical results with experimental data for 82 states in the region. Breaking rotational, time-reversal, and signature symmetries, we aligned the intrinsic angular momenta along the axis of axial symmetry, thereby enabling full shape- and spin-self-consistent polarizations. The spectroscopic moments were then obtained by restoring rotational symmetry. We conducted a detailed analysis of the pattern of agreement and disagreement between theory and experiment in individual nuclei. For the magnetic-dipole moments, agreement with the data varies and is characterized by an overall average and rms deviation of 0.11μN and 0.35μN, respectively. For the electric-quadrupole moments, a good corresponding agreement of 0.16 and 0.29 b was observed.

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Addendum to “Electromagnetic moments of ground and excited states calculated in heavy odd-N open-shell nuclei”

J. Dobaczewski, A. E. Stuchbery, G. Danneaux, A. Nagpal, P. L. Sassarini, and H. Wibowo
Phys. Rev. C 113, 044312 (2026)

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References (64)

  1. B. Castel and I. S. Towner, Modern Theories of Nuclear Moments (Clarendon Press, Oxford, 1990).
  2. G. Neyens, Nuclear magnetic and quadrupole moments for nuclear structure research on exotic nuclei, Rep. Prog. Phys. 66, 633 (2003).
  3. X. Yang, S. Wang, S. Wilkins, and R. G. Ruiz, Laser spectroscopy for the study of exotic nuclei, Prog. Part. Nucl. Phys. 129, 104005 (2023).
  4. P. L. Sassarini, J. Dobaczewski, J. Bonnard, and R. F. Garcia Ruiz, Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei, J. Phys. G: Nucl. Part. Phys. 49, 11LT01 (2022).
  5. J. Bonnard, J. Dobaczewski, G. Danneaux, and M. Kortelainen, Nuclear DFT electromagnetic moments in heavy deformed open-shell odd nuclei, Phys. Lett. B 843, 138014 (2023).
  6. H. Wibowo, B. C. Backes, J. Dobaczewski, R. P. de Groote, A. Nagpal, A. Sánchez-Fernández, X. Sun, and J. L. Wood, Electromagnetic moments in the Sn-Gd region determined within nuclear DFT, J. Phys. G: Nucl. Part. Phys. 52, 065104 (2025).
  7. S. Nilsson, Binding states of individual nucleons in strongly deformed nuclei, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955).
  8. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980).
  9. R. Bengtsson, J. Dudek, W. Nazarewicz, and P. Olanders, A systematic comparison between the Nilsson and Woods-Saxon deformed shell model potentials, Phys. Scr. 39, 196 (1989).
  10. J. Dobaczewski, P. Bączyk, P. Becker, M. Bender, K. Bennaceur, J. Bonnard, Y. Gao, A. Idini, M. Konieczka, M. Kortelainen, L. Próchniak, A. M. Romero, W. Satuła, Y. Shi, L. F. Yu, and T. R. Werner, Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h): A new version of the program, J. Phys. G: Nucl. Part. Phys. 48, 102001 (2021).
  11. J. Dobaczewski, et al., Code hfodd, version to be published (2026).
  12. A. Restrepo-Giraldo, et al., Code hfodd, the user guide, to be published (2026).
  13. A. Restrepo-Giraldo, et al., Radiative decay of the Th229 isomer determined within nuclear DFT (unpublished).
  14. B. Bally, B. Avez, M. Bender, and P.-H. Heenen, Beyond mean-field calculations for odd-mass nuclei, Phys. Rev. Lett. 113, 162501 (2014).
  15. B. Bally, G. Giacalone, and M. Bender, Structure of Xe128,129,130 through multi-reference energy density functional calculations, Eur. Phys. J. A 58, 187 (2022).
  16. B. Bally, G. Giacalone, and M. Bender, The shape of gold, Eur. Phys. J. A 59, 58 (2023).
  17. L. Bonneau, N. Minkov, D. D. Duc, P. Quentin, and J. Bartel, Effect of core polarization on magnetic dipole moments in deformed odd-mass nuclei, Phys. Rev. C 91, 054307 (2015).
  18. G. Co', V. De Donno, M. Anguiano, R. N. Bernard, and A. M. Lallena, Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach, Phys. Rev. C 92, 024314 (2015).
  19. M. Borrajo and J. L. Egido, A symmetry-conserving description of odd nuclei with the Gogny force, Eur. Phys. J. A 52, 277 (2016).
  20. M. Borrajo and J. L. Egido, Ground-state properties of even and odd magnesium isotopes in a symmetry-conserving approach, Phys. Lett. B 764, 328 (2017).
  21. J. Li and J. Meng, Nuclear magnetic moments in covariant density functional theory, Front. Phys. 13, 132109 (2018).
  22. S. Péru, S. Hilaire, S. Goriely, and M. Martini, Description of magnetic moments within the Gogny Hartree-Fock-Bogolyubov framework: Application to Hg isotopes, Phys. Rev. C 104, 024328 (2021).
  23. W. Ryssens, G. Scamps, S. Goriely, and M. Bender, Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking, Eur. Phys. J. A 58, 246 (2022).
  24. H. Nakada and H. Iwata, Magnetic dipole moments adjacent to doubly magic nuclei in self-consistent mean-field theory with realistic spin-isospin and tensor forces, Phys. Rev. C 113, 014315 (2026).
  25. J. A. Sheikh, J. Dobaczewski, P. Ring, L. M. Robledo, and C. Yannouleas, Symmetry restoration in mean-field approaches, J. Phys. G: Nucl. Part. Phys. 48, 123001 (2021).
  26. M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, and S. M. Wild, Nuclear energy density optimization: Large deformations, Phys. Rev. C 85, 024304 (2012).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4q99-rv67 for the description and examples of databases containing detailed results in numerical format, along with their respective plots, and instructions on retrieving the results obtained for the rotational bands.
  28. Repository of raw data obtained in this work is available at https://webfiles.york.ac.uk/HFODD/Projects/Gadolinium-Osmium.
  29. B. Wong, Points of view: Color blindness, Nat. Methods 8, 441 (2011).
  30. R. B. Firestone, et al., Table of Isotopes: 1999 Update, 8th ed. (Wiley, New York, 1999).
  31. D. Tarpanov, J. Dobaczewski, J. Toivanen, and B. G. Carlsson, Spectroscopic properties of nuclear Skyrme energy density functionals, Phys. Rev. Lett. 113, 252501 (2014).
  32. D. Tarpanov, J. Toivanen, J. Dobaczewski, and B. G. Carlsson, Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches, Phys. Rev. C 89, 014307 (2014).
  33. See Ref. [8], Eq. (11.143).
  34. A. Jungclaus, B. Binder, A. Dietrich, T. Härtlein, H. Bauer, C. Gund, D. Pansegrau, D. Schwalm, D. Bazzacco, E. Farnea, S. Lunardi, C. Rossi-Alvarez, C. Ur, G. de Angelis, A. Gadea, D. R. Napoli, X. R. Zhou, and Y. Sun, Excited bands and signature dependent electromagnetic decay properties in neutron-rich 159,161,163Dy, Phys. Rev. C 67, 034302 (2003).
  35. N. J. Stone, Table of recommended nuclear magnetic dipole moments: Part I - long-lived states, INDC International Nuclear Data Committee, report INDC(NDS)-0794 (IAEA, 2019), doi:10.61092/iaea.yjpc-cns6.
  36. N. J. Stone, Table of recommended nuclear magnetic dipole moments: Part II, short-lived states, INDC International Nuclear Data Committee, report INDC(NDS)-0816 (IAEA, 2020), doi:10.61092/iaea.1p48-p6c6.
  37. N. J. Stone, Table of nuclear electric quadrupole moments, INDC International Nuclear Data Committee, report INDC(NDS)-0833 (IAEA, 2021), doi:10.61092/iaea.a6te-dg7q.
  38. K.-G. Plingen, B. Wolbeck, and F.-J. Schröder, Hyperfine interaction in polycrystalline paramagnetic ytterbium oxide studied by the Mössbauer effect, Nucl. Phys. A 165, 97 (1971).
  39. J. Dobaczewski and J. Dudek, Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis I. The method, Comput. Phys. Comm. 102, 166 (1997).
  40. X. M. Feng, P. Wang, W. Yang, and G. R. Jin, High-precision evaluation of Wigner's d matrix by exact diagonalization, Phys. Rev. E 92, 043307 (2015).
  41. D. Varshalovich, A. Moskalev, and V. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
  42. S. C. Sylvester and D. Schroeer, Mössbauer effect following Coulomb excitation of the 43.8-keV state of Dy161, Phys. Rev. C 7, 2056 (1973).
  43. J. Ferch, W. Dankwort, and H. Gebauer, Hyperfine structure investigations in DyI with the atomic beam magnetic resonance method, Phys. Lett. A 49, 287 (1974).
  44. A. Bohr and B. R. Mottelson, Nuclear Structure (W. A. Benjamin, Reading, 1975), Vol. II.
  45. Evaluated Nuclear Structure Data File (ENSDF) located at the website (http://www.nndc.bnl.gov/ensdf/) of Brookhaven National Laboratory.
  46. To increase the readability of presentation, in Sec. 4, we explicitly added the parities π=(−1)N0 to the Nilsson labels [N0nzΛ]Kπ.
  47. R. Neugart, K. Wendt, S. A. Ahmad, W. Klempt, and C. Ekström, Nuclear moments and charge radii of rare-earth isotopes studied by collinear fast-beam laser spectroscopy, Hyperfine Interact. 15, 181 (1983).
  48. C. Schulz, E. Arnold, W. Borchers, W. Neu, R. Neugart, M. Neuroth, E. W. Otten, M. Scherf, K. Wendt, P. Lievens, Y. A. Kudryavtsev, V. S. Letokhov, V. I. Mishin, and V. V. Petrunin, Resonance ionization spectroscopy on a fast atomic ytterbium beam, J. Phys. B: At. Mol. Opt. Phys. 24, 4831 (1991).
  49. E. Dafni, J. Bendahan, C. Broude, G. Goldring, M. Hass, E. Lahmer-Naim, M. Rafailovich, N. De Campos, and A. Gelberg, G-factors of short-lived isomers in Gd147,148 and the role of the 3− core excitation, Phys. Lett. B 199, 26 (1987).
  50. O. Häusser, P. Taras, W. Trautmann, D. Ward, T. K. Alexander, H. R. Andrews, B. Haas, and D. Horn, g factors of high-spin yrast traps in Gd146,147, Phys. Rev. Lett. 42, 1451 (1979).
  51. D. B. Laubacher, Y. Tanaka, R. M. Steffen, E. B. Shera, and M. V. Hoehn, Muonic x-ray measurement of the monopole and quadrupole charge parameters of Gd154−158,160, Phys. Rev. C 27, 1772 (1983).
  52. P. Raghavan, Table of nuclear moments, At. Data Nucl. Data Tables 42, 189 (1989).
  53. C. Ekström, T. Noreland, M. Olsmats, and B. Wannberg, Nuclear spins of neutron-deficient holmium and erbium isotopes, Nucl. Phys. A 135, 289 (1969).
  54. C. M. Baglin and E. McCutchan, Nuclear data sheets for A=171, Nucl. Data Sheets 151, 334 (2018).
  55. N. Stone, Table of nuclear electric quadrupole moments, At. Data Nucl. Data Tables 111-112, 1 (2016).
  56. I. Ragnarsson and P. B. Semmes, Description of nuclear moments and nuclear spectra in the particle-rotor model, Hyperfine Interact. 43, 423 (1988).
  57. I. Alfter, E. Bodenstedt, W. Knichel, J. Schüth, and R. Vianden, g-factors of rotational states in Hf176, Hf177, and Hf180, Zeitschrift für Physik A Hadrons and Nuclei 355, 363 (1996).
  58. A. Nieminen, P. Campbell, J. Billowes, D. H. Forest, J. A. R. Griffith, J. Huikari, A. Jokinen, I. D. Moore, R. Moore, G. Tungate, and J. Äystö, On-line ion cooling and bunching for collinear laser spectroscopy, Phys. Rev. Lett. 88, 094801 (2002).
  59. W. Nazarewicz, M. Riley, and J. Garrett, Equilibrium deformations and excitation energies of single-quasiproton band heads of rare-earth nuclei, Nucl. Phys. A 512, 61 (1990).
  60. P. C. Joshi and P. C. Sood, Coriolis perturbation effects for Kπ=32− bands in odd-neutron rare-earth nuclei, Phys. Rev. C 9, 1965 (1974).
  61. A. Stuchbery, G. Lampard, and H. Bolotin, Spectroscopy of Gd155 following Coulomb excitation: Signature-independent M1 properties and evidence for octupole correlations, Nucl. Phys. A 642, 361 (1998).
  62. A. E. Stuchbery, Magnetic properties of rotational states in the pseudo-Nilsson model, Nucl. Phys. A 700, 83 (2002).
  63. T. Miyagi, X. Cao, R. Seutin, S. Bacca, R. F. Garcia Ruiz, K. Hebeler, J. D. Holt, and A. Schwenk, Impact of two-body currents on magnetic dipole moments of nuclei, Phys. Rev. Lett. 132, 232503 (2024).
  64. H. Wibowo, R. Han, B. C. Backes, G. Danneaux, J. Dobaczewski, W. Jiang, and M. Kortelainen, The nuclear DFT two-body meson-exchange contributions to the magnetic dipole moments of atomic nuclei (unpublished).

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Phys. Rev. C 113, 024306– Published 5 February, 2026
  • Received 6 October 2025
  • Accepted 10 December 2025
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