- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Charge Radii Measurements of Exotic Tin Isotopes in the Proximity of N=50 and N=82

F. P. Gustafsson1,2,*, L. V. Rodríguez3,2,4,†, R. F. Garcia Ruiz5,6,2,‡, T. Miyagi7,8,9,3, S. W. Bai10, D. L. Balabanski11, C. L. Binnersley6, M. L. Bissell6, K. Blaum3 et al.

B. Cheal12, T. E. Cocolios1, G. J. Farooq-Smith1, K. T. Flanagan6,13, S. Franchoo4, A. Galindo-Uribarri14,15, G. Georgiev4, W. Gins1, C. Gorges8, R. P. de Groote1, H. Heylen2, J. D. Holt16,17, A. Kanellakopoulos1, J. Karthein5,§, S. Kaufmann8, Á. Koszorús1, K. König8, V. Lagaki2,18, S. Lechner2,19, B. Maass8, S. Malbrunot-Ettenauer2, W. Nazarewicz20, R. Neugart21,3, G. Neyens1,2, W. Nörtershäuser8, T. Otsuka22,1,23,24,25, P.-G. Reinhard26, N. Rondelez1, E. Romero-Romero14,15, C. M. Ricketts6, S. Sailer27, R. Sánchez28, S. Schmidt8, A. Schwenk8,9,3, S. R. Stroberg16,29,30, N. Shimizu7, Y. Tsunoda22, A. R. Vernon5, L. Wehner21, S. G. Wilkins5, C. Wraith12, L. Xie6, Z. Y. Xu1, X. F. Yang10, and D. T. Yordanov3,4,2

  • 1Instituut voor Kern- en Stralingsfysica, KU Leuven, 3001 Leuven, Belgium
  • 2CERN, 1211 Geneva 23, Switzerland
  • 3Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
  • 4IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France
  • 5Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 6School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom
  • 7Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
  • 8Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
  • 9ExtreMe Matter Institute, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
  • 10School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
  • 11ELI-NP, Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, 077125 Magurele, Romania
  • 12Oliver Lodge Laboratory, Oxford Street, University of Liverpool, Liverpool L69 7ZE, United Kingdom
  • 13Photon Science Institute, Alan Turing Building, The University of Manchester, Manchester, M13 9PY, United Kingdom
  • 14Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
  • 15Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
  • 16TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
  • 17Department of Physics, McGill University, Montréal, Quebec H3A 2T8, Canada
  • 18Institut für Physik, Universität Greifswald, 17487 Greifswald, Germany
  • 19Technische Universität Wien, Karlsplatz 13, 1040 Wien, Austria
  • 20Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA
  • 21Institut für Kernchemie, Universität Mainz, 55128 Mainz, Germany
  • 22Center for Nuclear Study, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 23Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 24RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • 25National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
  • 26Institut für Theoretische Physik, Friedrich-Alexander-Universität, Erlangen/Nürnberg, Germany
  • 27Technische Universität München, 80333 Munich, Germany
  • 28GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
  • 29Department of Physics, University of Washington, Seattle, Washington, USA
  • 30Physics Division, Argonne National Laboratory, Lemont, Illinois, USA

  • *Contact author: fredrik.parnefjord.gustafsson@cern.ch
  • †Contact author: liss.vazquez.rodriguez@cern.ch
  • ‡Contact author: rgarciar@mit.edu
  • §Present Address: Texas A&M University, Cyclotron Institute/Department of Physics and Astronomy, College Station, Texas 77840, USA.
PDF

Phys. Rev. Lett. 135, 222501 – Published 25 November, 2025

DOI: https://doi.org/10.1103/wbdx-k3cd

Abstract

We report nuclear charge radii for the isotopes Sn104–134, measured using two different collinear laser spectroscopy techniques at ISOLDE-CERN. These measurements clarify the archlike trend in charge radii along the isotopic chain and reveal an odd-even staggering that is more pronounced near the N=50 and N=82 shell closures. The observed local trends are well described by both nuclear density functional theory and valence space in-medium similarity renormalization group calculations. Both theories predict appreciable contributions from beyond-mean-field correlations to the charge radii of the neutron-deficient tin isotopes. The models, however, fall short of reproducing the magnitude of the known B(E2) transition probabilities, highlighting the remaining challenges in achieving a unified description of both ground-state properties and collective phenomena.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (81)

  1. C. B. Hinke, M. Böhmer, P. Boutachkov, T. Faestermann, H. Geissel, J. Gerl, R. Gernhäuser, M. Górska, A. Gottardo, H. Grawe et al., Superallowed Gamow–Teller decay of the doubly magic nucleus Sn100, Nature (London) 486, 341 (2012).
  2. T. D. Morris, J. Simonis, S. R. Stroberg, C. Stumpf, G. Hagen, J. D. Holt, G. R. Jansen, T. Papenbrock, R. Roth, and A. Schwenk, Structure of the lightest tin isotopes, Phys. Rev. Lett. 120, 152503 (2018).
  3. T. Togashi, Y. Tsunoda, T. Otsuka, N. Shimizu, and M. Honma, Novel shape evolution in Sn isotopes from magic numbers 50 to 82, Phys. Rev. Lett. 121, 062501 (2018).
  4. P. Gysbers, G. Hagen, J. D. Holt, G. R. Jansen, T. D. Morris, P. Navrátil, T. Papenbrock, S. Quaglioni, A. Schwenk, S. R. Stroberg, and K. A. Wendt, Discrepancy between experimental and theoretical β-decay rates resolved from first principles, Nat. Phys. 15, 428 (2019).
  5. M. Mougeot, D. Atanasov, J. Karthein, R. N. Wolf, P. Ascher, K. Blaum, K. Chrysalidis, G. Hagen, J. D. Holt, W. J. Huang et al., Mass measurements of In99–101 challenge ab initio nuclear theory of the nuclide Sn100, Nat. Phys. 17, 1099 (2021).
  6. A. Tichai, P. Demol, and T. Duguet, Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory, Phys. Lett. B 851, 138571 (2024).
  7. P. Arthuis, K. Hebeler, and A. Schwenk, Neutron-rich nuclei and neutron skins from chiral low-resolution interactions, arXiv:2401.06675.
  8. K. L. Jones, A. S. Adekola, D. W. Bardayan, J. C. Blackmon, K. Y. Chae, K. A. Chipps, J. A. Cizewski, L. Erikson, C. Harlin, R. Hatarik et al., The magic nature of Sn132 explored through the single-particle states of Sn133, Nature (London) 465, 454 (2010).
  9. D. Rosiak, M. Seidlitz, P. Reiter, H. Naïdja, Y. Tsunoda, T. Togashi, F. Nowacki, T. Otsuka, G. Colò, K. Arnswald et al. (MINIBALL and HIE-ISOLDE Collaborations), Enhanced quadrupole and octupole strength in doubly magic Sn132, Phys. Rev. Lett. 121, 252501 (2018).
  10. C. Gorges, L. V. Rodríguez, D. L. Balabanski, M. L. Bissell, K. Blaum, B. Cheal, R. F. Garcia Ruiz, G. Georgiev, W. Gins, H. Heylen et al., Laser spectroscopy of neutron-rich tin isotopes: A discontinuity in charge radii across the N=82 shell closure, Phys. Rev. Lett. 122, 192502 (2019).
  11. L. V. Rodríguez, D. L. Balabanski, M. L. Bissell, K. Blaum, B. Cheal, G. De Gregorio, J. Ekman, R. F. Garcia Ruiz, A. Gargano, G. Georgiev et al., Doubly-magic character of Sn132 studied via electromagnetic moments of Sn133, Phys. Rev. C 102, 051301 (2020).
  12. A. R. Vernon, R. F. Garcia Ruiz, T. Miyagi, C. L. Binnersley, J. Billowes, M. L. Bissell, J. Bonnard, T. E. Cocolios, J. Dobaczewski, G. J. Farooq-Smith et al., Nuclear moments of indium isotopes reveal abrupt change at magic number 82, Nature (London) 607, 260 (2022).
  13. D. Seweryniak, M. P. Carpenter, S. Gros, A. A. Hecht, N. Hoteling, R. V. F. Janssens, T. L. Khoo, T. Lauritsen, C. J. Lister, G. Lotay et al., Single-neutron states in Sn101, Phys. Rev. Lett. 99, 022504 (2007).
  14. I. G. Darby, R. K. Grzywacz, J. C. Batchelder, C. R. Bingham, L. Cartegni, C. J. Gross, M. Hjorth-Jensen, D. T. Joss, S. N. Liddick, W. Nazarewicz et al., Orbital dependent nucleonic pairing in the lightest known isotopes of tin, Phys. Rev. Lett. 105, 162502 (2010).
  15. A. Banu, J. Gerl, C. Fahlander, M. Górska, H. Grawe, T. R. Saito, H.-J. Wollersheim, E. Caurier, T. Engeland, A. Gniady et al., Sn108 studied with intermediate-energy Coulomb excitation, Phys. Rev. C 72, 061305 (2005).
  16. C. Vaman, C. Andreoiu, D. Bazin, A. Becerril, B. A. Brown, C. M. Campbell, A. Chester, J. M. Cook, D. C. Dinca, A. Gade et al., Z=50 Shell gap near Sn100 from intermediate-energy Coulomb excitations in even-mass Sn106–112 isotopes, Phys. Rev. Lett. 99, 162501 (2007).
  17. M. Reponen, R. P. de Groote, L. Al Ayoubi, O. Beliuskina, M. L. Bissell, P. Campbell, L. Cañete, B. Cheal, K. Chrysalidis, C. Delafosse et al., Evidence of a sudden increase in the nuclear size of proton-rich silver-96, Nat. Commun. 12, 4596 (2021).
  18. L. Nies, D. Atanasov, M. Athanasakis-Kaklamanakis, M. Au, K. Blaum, J. Dobaczewski, B. S. Hu, J. D. Holt, J. Karthein, I. Kulikov et al., Isomeric excitation energy for In99m from mass spectrometry reveals constant trend next to doubly magic Sn100, Phys. Rev. Lett. 131, 022502 (2023).
  19. Z. Ge, M. Reponen, T. Eronen, B. Hu, M. Kortelainen, A. Kankainen, I. Moore, D. Nesterenko, C. Yuan, O. Beliuskina et al., High-precision mass measurements of neutron deficient silver isotopes probe the robustness of the N=50 shell closure, Phys. Rev. Lett. 133, 132503 (2024).
  20. T. Bäck, C. Qi, B. Cederwall, R. Liotta, F. Ghazi Moradi, A. Johnson, R. Wyss, and R. Wadsworth, Transition probabilities near Sn100 and the stability of the Z, N=50 shell closure, Phys. Rev. C 87, 031306 (2013).
  21. G. Guastalla, D. D. DiJulio, M. Górska, J. Cederkäll, P. Boutachkov, P. Golubev, S. Pietri, H. Grawe, F. Nowacki, K. Sieja et al., Coulomb excitation of Sn104 and the strength of the Sn100 shell closure, Phys. Rev. Lett. 110, 172501 (2013).
  22. P. Doornenbal, S. Takeuchi, N. Aoi, M. Matsushita, A. Obertelli, D. Steppenbeck, H. Wang, L. Audirac, H. Baba, P. Bednarczyk et al., Intermediate-energy coulomb excitation of Sn104: Moderate E2 strength decrease approaching Sn100, Phys. Rev. C 90, 061302 (2014).
  23. J. Karthein, C. M. Ricketts, R. F. Garcia Ruiz, J. Billowes, C. L. Binnersley, T. E. Cocolios, J. Dobaczewski, G. J. Farooq-Smith, K. T. Flanagan, G. Georgiev et al., Electromagnetic properties of indium isotopes illuminate the doubly magic character of Sn100, Nat. Phys. 20, 1719 (2024).
  24. 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).
  25. Á. Koszorús, J. Billowes, C. Binnersley, M. Bissell, T. Cocolios, B. Cooper, R. de Groote, G. Farooq-Smith, V. Fedosseev, K. Flanagan et al., Resonance ionization schemes for high resolution and high efficiency studies of exotic nuclei at the CRIS experiment, Nucl. Instrum. Methods Phys. Res., Sect. B 463, 398 (2020).
  26. F. L. Blanc, L. Cabaret, E. Cottereau, J. E. Crawford, S. Essabaa, J. Genevey, R. Horn, G. Huber, J. Lassen, J. K. P. Lee et al., Charge-radius change and nuclear moments in the heavy tin isotopes from laser spectroscopy: Charge radius of Sn132, Phys. Rev. C 72, 034305 (2005).
  27. J. Eberz, U. Dinger, G. Huber, H. Lochmann, R. Menges, G. Ulm, R. Kirchner, O. Klepper, T. U. Kühl, and D. Marx, Nuclear spins, moments and charge radii of Sn108–111, Z. Phys. A 326, 121 (1987).
  28. M. Anselment, K. Bekk, A. Hanser, H. Hoeffgen, G. Meisel, S. Göring, H. Rebel, and G. Schatz, Charge radii and moments of tin nuclei by laser spectroscopy, Phys. Rev. C 34, 1052 (1986).

  29. We note that Fig. 7 of Ref. [30] contains a data point for the charge radius of Sn133. This has been a tentative estimate, not based on actual measurement, and was unfortunately not removed from the final version of the paper.

  30. P.-G. Reinhard, J. O’Neal, S. M. Wild, and W. Nazarewicz, Extended Fayans energy density functional: Optimization and analysis, J. Phys. G 51, 105101 (2024).
  31. M. Bender, P.-H. Heenen, and P.-G. Reinhard, Self-consistent mean-field models for nuclear structure, Rev. Mod. Phys. 75, 121 (2003).
  32. Energy Density Functional Methods for Atomic Nuclei, edited by N. Schunck (IOP Publishing, Bristol, UK, 2019), pp. 2053–2563.
  33. H. Hergert, S. Bogner, T. Morris, A. Schwenk, and K. Tsukiyama, The in-medium similarity renormalization group: A novel ab initio method for nuclei, Phys. Rep. 621, 165 (2016).
  34. S. R. Stroberg, H. Hergert, S. K. Bogner, and J. D. Holt, Nonempirical interactions for the nuclear shell model: An update, Annu. Rev. Nucl. Part. Sci. 69, 307 (2019).
  35. F. P. Gustafsson, C. M. Ricketts, M. L. Reitsma, R. F. Garcia Ruiz, S. W. Bai, J. C. Berengut, J. Billowes, C. L. Binnersley, A. Borschevsky, T. E. Cocolios et al., Tin resonance-ionization schemes for atomic- and nuclear-structure studies, Phys. Rev. A 102, 052812 (2020).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/wbdx-k3cd for the VS-IMSRG calculations and the experimental methodology for determining nuclear charge radii with the tabulated isotope shift results.
  37. D. T. Yordanov, L. V. Rodríguez, D. L. Balabanski, J. Bieroń, M. L. Bissell, K. Blaum, B. Cheal, J. Ekman, G. Gaigalas, R. F. Garcia Ruiz et al., Structural trends in atomic nuclei from laser spectroscopy of tin, Commun. Phys. 3, 107 (2020).
  38. G. Fricke and K. Heilig, Nuclear charge radii·50-Sn tin, in Nuclear Charge Radii, Datasheet from Landolt-Börnstein—Group I Elementary Particles, Nuclei and Atoms (Springer Materials) Vol. 20 (Springer-Verlag, Berlin, Heidelberg, 2004), 10.1007/10856314_52.
  39. D. R. Entem and R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory, Phys. Rev. C 68, 041001 (2003).
  40. K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Improved nuclear matter calculations from chiral low-momentum interactions, Phys. Rev. C 83, 031301 (2011).
  41. W. G. Jiang, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Accurate bulk properties of nuclei from A=2 to ∞ from potentials with Δ isobars, Phys. Rev. C 102, 054301 (2020).
  42. S. R. Stroberg, J. D. Holt, A. Schwenk, and J. Simonis, Ab initio limits of atomic nuclei, Phys. Rev. Lett. 126, 022501 (2021).
  43. R. P. de Groote, J. Billowes, C. L. Binnersley, M. L. Bissell, T. E. Cocolios, T. Day Goodacre, G. J. Farooq-Smith, D. V. Fedorov, K. T. Flanagan, S. Franchoo et al., Measurement and microscopic description of odd–even staggering of charge radii of exotic copper isotopes, Nat. Phys. 16, 620 (2020).
  44. J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Saturation with chiral interactions and consequences for finite nuclei, Phys. Rev. C 96, 014303 (2017).
  45. P.-G. Reinhard, B. Schuetrumpf, and J. Maruhn, The axial Hartree-Fock + BCS code skyax, Comput. Phys. Commun. 258, 107603 (2021).
  46. K. J. Pototzky, J. Erler, P.-G. Reinhard, and V. O. Nesterenko, Properties of odd nuclei and the impact of time-odd mean fields: A systematic Skyrme-Hartree-Fock analysis, Eur. Phys. J. A 46, 299 (2010).
  47. P. Klüpfel, P.-G. Reinhard, T. J. Bürvenich, and J. A. Maruhn, Variations on a theme by Skyrme: A systematic study of adjustments of model parameters, Phys. Rev. C 79, 034310 (2009).
  48. A. J. Miller, K. Minamisono, A. Klose, D. Garand, C. Kujawa, J. D. Lantis, Y. Liu, B. Maaß, P. F. Mantica, W. Nazarewicz et al., Proton superfluidity and charge radii in proton-rich calcium isotopes, Nat. Phys. 15, 432 (2019).
  49. P.-G. Reinhard and W. Nazarewicz, Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii, Phys. Rev. C 103, 054310 (2021).
  50. J. Dobaczewski, W. Nazarewicz, and P.-G. Reinhard, Error estimates of theoretical models: A guide, J. Phys. G 41, 074001 (2014).
  51. P. Klüpfel, J. Erler, P.-G. Reinhard, and J. A. Maruhn, Systematics of collective correlation energies from self-consistent mean-field calculations, Eur. Phys. J. A 37, 343 (2008).
  52. P.-G. Reinhard and W. Nazarewicz, Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach, Phys. Rev. C 93, 051303 (2016).
  53. P.-G. Reinhard and W. Nazarewicz, Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional, Phys. Rev. C 95, 064328 (2017).
  54. T. Miyagi, S. R. Stroberg, J. D. Holt, and N. Shimizu, Ab initio multishell valence-space Hamiltonians and the island of inversion, Phys. Rev. C 102, 034320 (2020).
  55. C. Qi and Z. X. Xu, Monopole-optimized effective interaction for tin isotopes, Phys. Rev. C 86, 044323 (2012).
  56. D. C. Radford, C. Baktash, J. R. Beene, B. Fuentes, A. Galindo-Uribarri, G. J., C. J. Gross, M. L. Halbert, Y. Larochelle, T. A. Lewis et al., Nuclear structure studies with heavy neutron-rich RIBS at the HRIBF, Nucl. Phys. A746, 83 (2004).
  57. A. Ekström, J. Cederkäll, C. Fahlander, M. Hjorth-Jensen, F. Ames, P. A. Butler, T. Davinson, J. Eberth, F. Fincke, A. Görgen et al., 0gs+→21+ Transition strengths in Sn106 and Sn108, Phys. Rev. Lett. 101, 012502 (2008).
  58. J. M. Allmond, D. C. Radford, C. Baktash, J. C. Batchelder, A. Galindo-Uribarri, C. J. Gross, P. A. Hausladen, K. Lagergren, Y. Larochelle, E. Padilla-Rodal, and C.-H. Yu, Coulomb excitation of Sn124,126,128, Phys. Rev. C 84, 061303 (2011).
  59. R. L. Varner, J. R. Beene, C. Baktash, A. Galindo-Uribarri, C. J. Gross, J. Gomez del Campo, M. L. Halbert, P. A. Hausladen, Y. Larochelle, J. F. Liang et al., Coulomb excitation measurements of transition strengths in the isotopes Sn132,134, Eur. Phys. J. A 25, 391 (2005).
  60. P. H. Stelson, F. K. McGowan, R. L. Robinson, and W. T. Milner, Static quadrupole moment of the first 2+ states of the even tin nuclei, Phys. Rev. C 2, 2015 (1970).
  61. M. Siciliano, J. Valiente-Dobón, A. Goasduff, F. Nowacki, A. Zuker, D. Bazzacco, A. Lopez-Martens, E. Clément, G. Benzoni, T. Braunroth et al., Pairing-quadrupole interplay in the neutron-deficient tin nuclei: First lifetime measurements of low-lying states in Sn106,108, Phys. Lett. B 806, 135474 (2020).
  62. J. Beene, R. Varner, C. Baktash, A. Galindo-Uribarri, C. Gross, J. Gomez del Campo, M. Halbert, P. Hausladen, Y. Larochelle, J. Liang et al., Coulomb excitation studies of Sn132,134, Nucl. Phys. A746, 471 (2004).
  63. D. Radford, C. Baktash, C. Barton, J. Batchelder, J. Beene, C. Bingham, M. Caprio, M. Danchev, B. Fuentes, A. Galindo-Uribarri et al., Coulomb excitation and transfer reactions with rare neutron-rich isotopes, Nucl. Phys. A752, 264 (2005).
  64. B. Pritychenko, M. Birch, B. Singh, and M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even-even nuclei, At. Data Nucl. Data Tables 107, 1 (2016).
  65. S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S. K. Bogner, R. Roth, and A. Schwenk, Nucleus-dependent valence-space approach to nuclear structure, Phys. Rev. Lett. 118, 032502 (2017).
  66. B. H. Sun, C. Y. Liu, and H. X. Wang, Correlating double-difference of charge radii with quadrupole deformation and B(E2) in atomic nuclei, Phys. Rev. C 95, 014307 (2017).
  67. M. A. Caprio, P. J. Fasano, and P. Maris, Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius, Phys. Rev. C 105, L061302 (2022).
  68. T. Otsuka, N. Shimizu, and Y. Tsunoda, Moments and radii of exotic Na and Mg isotopes, Phys. Rev. C 105, 014319 (2022).
  69. B. A. Brown and K. Minamisono, β2-corrections to spherical energy-density functional calculations for root-mean-square charge radii, Phys. Rev. C 106, L011304 (2022).
  70. J. Henderson, G. Hackman, P. Ruotsalainen, S. Stroberg, K. Launey, J. Holt, F. Ali, N. Bernier, M. Bentley, M. Bowry et al., Testing microscopically derived descriptions of nuclear collectivity: Coulomb excitation of Mg22, Phys. Lett. B 782, 468 (2018).
  71. S. R. Stroberg, J. Henderson, G. Hackman, P. Ruotsalainen, G. Hagen, and J. D. Holt, Systematics of E2 strength in the sd shell with the valence-space in-medium similarity renormalization group, Phys. Rev. C 105, 034333 (2022).
  72. N. M. Parzuchowski, S. R. Stroberg, P. Navrátil, H. Hergert, and S. K. Bogner, Ab initio electromagnetic observables with the in-medium similarity renormalization group, Phys. Rev. C 96, 034324 (2017).
  73. S. Lechner, T. Miyagi, Z. Xu, M. Bissell, K. Blaum, B. Cheal, C. Devlin, R. Garcia Ruiz, J. Ginges, H. Heylen et al., Electromagnetic moments of the antimony isotopes Sn112–133, Phys. Lett. B 847, 138278 (2023).
  74. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  75. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright et al., scipy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  76. The Pandas Development Team, pandas-dev/pandas: pandas, Zenodo, v2.3.3, 10.5281/zenodo.17229934 (2023).
  77. Wes McKinney, Data structures for statistical computing in python, in Proceedings of the 9th python in Science Conference, edited by Stéfan van der Walt and Jarrod Millman (2010), pp. 56–61, 10.25080/Majora-92bf1922-00a.
  78. H. Dembinski et al., scikit-hep/iminuit (2023).
  79. F. James and M. Roos, minuit: A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10, 343 (1975).
  80. P. Müller, and W. Nörtershäuser, The qspec python package: A physics toolbox for laser spectroscopy, Comput. Phys. Commun. 311, 109550 (2025).
  81. J. D. Hunter, matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).

Outline

Information

Phys. Rev. Lett. 135, 222501– Published 25 November, 2025
  • Received 23 April 2025
  • Revised 1 September 2025
  • Accepted 24 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation