- 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

Fingerprints of Triaxiality in the Charge Radii of Neutron-Rich Ruthenium

Bernhard Maass1,2,*, Wouter Ryssens3,4,†, Kristian König2, Michael Bender5, Daniel P. Burdette1, Jason Clark1, Adam Dockery6,7, Guilherme Grams3, Max Horst2 et al.

Phillip Imgram2, Kei Minamisono6,7, Patrick Müller2, Peter Müller1, Wilfried Nörtershäuser2, Skyy V. Pineda6,8, Simon Rausch2, Laura Renth2, Brooke J. Rickey6,7, Daniel Santiago-Gonzalez1, Guy Savard1, Felix Sommer2, and Adrian A. Valverde1

  • *Contact author: maass@anl.gov
  • †Contact author: wouter.ryssens@ulb.be
PDF

Phys. Rev. Lett. 135, 202501 – Published 10 November, 2025

DOI: https://doi.org/10.1103/81h5-wjkd

Abstract

We present the first measurements with a new collinear laser spectroscopy setup at the Argonne Tandem Linac Accelerator System, utilizing its unique capability to deliver neutron-rich refractory metal isotopes produced by the spontaneous fission of Cf252. We measured isotope shifts from optical spectra for nine radioactive ruthenium isotopes Ru106–114, reaching deep into the mid-shell region. The extracted charge radii are in excellent agreement with predictions from the Brussels-Skyrme-on-a-Grid models that account for the triaxial deformation of nuclear ground states. We show that triaxial deformation impacts charge radii in models that feature shell effects, in contrast to what could be concluded from a liquid drop analysis. This indicates that this exotic type of deformation should not be neglected in regions where it is known to occur, even if its presence cannot be unambiguously inferred through laser spectroscopy.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (67)

  1. J. Bonn, G. Huber, H. J. Kluge, and E. W. Otten, Sudden change in the nuclear charge distribution of very light mercury isotopes, Phys. Lett. 38B, 308 (1972).
  2. C. Thibault et al., Hyperfine structure and isotope shift of the D2 line of Rb76–98 and some of their isomers, Phys. Rev. C 23, 2720 (1981).
  3. F. Buchinger et al., Systematics of nuclear ground state properties in Sr78–100 by laser spectroscopy, Phys. Rev. C 41, 2883 (1990).
  4. B. Cheal et al., The shape transition in the neutron-rich yttrium isotopes and isomers, Phys. Lett. B 645, 133 (2007).
  5. J. G. Cubiss et al., Charge radii and electromagnetic moments of At195–211, Phys. Rev. C 97, 054327 (2018).
  6. S. Sels et al., Shape staggering of midshell mercury isotopes from in-source laser spectroscopy compared with density-functional-theory and Monte Carlo shell-model calculations, Phys. Rev. C 99, 044306 (2019).
  7. A. Barzakh et al., Large shape staggering in neutron-deficient Bi isotopes, Phys. Rev. Lett. 127, 192501 (2021).
  8. G. Scamps, S. Goriely, E. Olsen, M. Bender, and W. Ryssens, Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: Effect of triaxial shape, Eur. Phys. J. A 57, 333 (2021).
  9. See Supplemental Material, which includes Refs. [10–15], at http://link.aps.org/supplemental/10.1103/81h5-wjkd for details of the fit and the King-plot procedure, the parametrization of nuclear shape, the BSkG models and the calculation of charge radii, and a more general treatise of triaxiality in the liquid-drop and BSkG models.
  10. E. C. Seltzer, K X-ray isotope shifts, Phys. Rev. 188, 1916 (1969).
  11. B. K. Sahoo et al., Analytic response relativistic coupled-cluster theory: The first application to indium isotope shifts, New J. Phys. 22, 012001 (2020).
  12. S. Raman, C. W. Nestor, and P. Tikkanen, Transition probability from the ground to the first excited 2+ state of even-even nuclides, At. Data Nucl. Data Tables 78, 1 (2001).
  13. W. Ryssens, Symmetry breaking in nuclear mean-field models, Ph. D. thesis, Université Libre de Bruxelles, Brussels, 2016.
  14. J. Srebrny et al., Experimental and theoretical investigations of quadrupole collective degrees of freedom in Ru104, Nucl. Phys. A766, 25 (2006).
  15. National Nuclear Data Center, Information extracted from the NuDat database (accessed 2025), https://www.nndc.bnl.gov/nudat3/.
  16. D. J. Rowe and J. L. Wood, Fundamentals of Nuclear Models (World Scientific, Singapore, 2010).
  17. D. Cline, Nuclear Shapes studied by Coulomb excitation, Annu. Rev. Nucl. Part. Sci. 36, 683 (1986).
  18. D. P. Grechukhin, Some experimental possibilities for verification of the model of nonaxial nuclei rotational spectrum, Sov. Phys. JETP 11, 1359 (1960), http://jetp.ras.ru/cgi-bin/e/index/e/11/6/p1359?a=list.
  19. D. P. Grechukhin, Correction to the article by D. P. Grechukhin “some experimental possibilities for verification of the model of nonaxial nuclei rotational spectrum,” Sov. Phys. JETP 13, 261 (1960), http://jetp.ras.ru/cgi-bin/e/index/e/13/1/p261?a=list.
  20. T. Hilberath, S. Becker, G. Bollen, H. J. Kluge, U. Krönert, G. Passler, J. Rikovska, and R. Wyss (The ISOLDE Collaboration), Ground-state properties of neutron-deficient platinum isotopes, Z. Phys. A 342, 1 (1992).
  21. P. E. Garrett et al., Coulomb excitation of Ru102 with C12 and O16, Phys. Rev. C 106, 064307 (2022).
  22. A. Esmaylzadeh et al., Investigation of γ softness: Lifetime measurements in Ru104,106, Phys. Rev. C 106, 064323 (2022).
  23. K. Sümmerer, N. Kaffrell, E. Stender, N. Trautmann, K. Brodén, G. Skarnemark, T. Björnstad, I. Haldorsen, and J. Maruhn, Levels in Ru106 and Ru108, Nucl. Phys. A339, 74 (1980).
  24. J. Äystö et al., Collective structure of the neutron-rich nuclei, Ru110 and Ru112, Nucl. Phys. A515, 365 (1990).
  25. J. A. Shannon et al., The role of triaxiality in the ground states of even-even neutron-rich Ru isotopes, Phys. Lett. B 336, 136 (1994).
  26. D. T. Doherty et al., Triaxiality near the Ru110 ground state from Coulomb excitation, Phys. Lett. B 766, 334 (2017).
  27. P. Möller, R. Bengtsson, B. G. Carlsson, P. Olivius, and T. Ichikawa, Global calculations of ground-state axial shape asymmetry of nuclei, Phys. Rev. Lett. 97, 162502 (2006).
  28. P. Möller, R. Bengtsson, B. Carlsson, P. Olivius, T. Ichikawa, H. Sagawa, and A. Iwamoto, Axial and reflection asymmetry of the nuclear ground state, At. Data Nucl. Data Tables 94, 758 (2008).
  29. S. Hilaire and M. Girod, The AMEDEE nuclear structure database, 10.1051/ndata:07709(2007).
  30. K. Nomura, R. Rodríguez-Guzmán, and L. M. Robledo, Structural evolution in A≈100 nuclei within the mapped interacting boson model based on the Gogny energy density functional, Phys. Rev. C 94, 044314 (2016).
  31. C. L. Zhang, G. H. Bhat, W. Nazarewicz, J. A. Sheikh, and Y. Shi, Theoretical study of triaxial shapes of neutron-rich Mo and Ru nuclei, Phys. Rev. C 92, 034307 (2015).
  32. 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).
  33. G. Grams, W. Ryssens, G. Scamps, S. Goriely, and N. Chamel, Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: III. From atomic nuclei to neutron stars, Eur. Phys. J. A 59, 270 (2023).
  34. G. Grams, N. N. Shchechilin, A. Sánchez-Fernández, W. Ryssens, N. Chamel, and S. Goriely, Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IV. Improved description of the isospin dependence of pairing, Eur. Phys. J. A 61, 35 (2025).
  35. W. Hukkanen et al., Binding energies of ground and isomeric states in neutron-rich ruthenium isotopes: Measurements at JYFLTRAP and comparison to theory, Phys. Rev. C 108, 064315 (2023).
  36. M. Hukkanen et al., Odd-odd neutron-rich rhodium isotopes studied with the double Penning trap JYFLTRAP, Phys. Rev. C 107, 014306 (2023).
  37. M. Stryjczyk et al., Discovery of a new long-lived isomer in Rh114 via Penning-trap mass spectrometry, Phys. Lett. B 862, 139359 (2025).
  38. G. Savard, A. F. Levand, and B. J. Zabransky, The CARIBU gas catcher, Nucl. Instrum. Methods Phys. Res., Sect. B 376, 246 (2016).
  39. G. Savard, S. Baker, C. Davids, A. F. Levand, E. F. Moore, R. C. Pardo, R. Vondrasek, B. J. Zabransky, and G. Zinkann, Radioactive beams from gas catchers: The CARIBU facility, Nucl. Instrum. Methods Phys. Res., Sect. B 266, 4086 (2008).
  40. G. Savard et al., CARIBU: A new facility for the study of neutron-rich isotopes, Hyperfine Interact. 199, 301 (2011).
  41. A. A. Valverde, M. Brodeur, J. A. Clark, D. Lascar, and G. Savard, A cooler-buncher for the N=126 factory at Argonne National Laboratory, Nucl. Instrum. Methods Phys. Res., Sect. B 463, 330 (2020).
  42. D. P. Burdette et al., Off-line Commissioning of the St. Benedict Radiofrequency Quadrupole Cooler-Buncher, arXiv:2504.08021.
  43. B. Barquest, G. Bollen, P. Mantica, K. Minamisono, R. Ringle, S. Schwarz, and C. Sumithrarachchi, RFQ beam cooler and buncher for collinear laser spectroscopy of rare isotopes, Nucl. Instrum. Methods Phys. Res., Sect. A 866, 18 (2017).
  44. A. Lapierre et al., First two operational years of the electron-beam ion trap charge breeder at the National Superconducting Cyclotron Laboratory, Phys. Rev. Accel. Beams 21, 053401 (2018).
  45. A. Nieminen et al., On-line ion cooling and bunching for collinear laser spectroscopy, Phys. Rev. Lett. 88, 094801 (2002).
  46. S. Passon, K. König, F. Schilling, B. Maaß, J. Meisner, and W. Nörtershäuser, Ultra-stable 3D-printed precision voltage divider for calibrations and experiments, Meas. Sens. 38, 101818 (2025).
  47. M. Verlinde et al., On the performance of wavelength meters: Part 1—consequences for medium-to-high-resolution laser spectroscopy, Appl. Phys. B 126, 85 (2020).
  48. K. König, P. Imgram, J. Krämer, B. Maaß, K. Mohr, T. Ratajczyk, F. Sommer, and W. Nörtershäuser, On the performance of wavelength meters: Part 2—frequency-comb based characterization for more accurate absolute wavelength determinations, Appl. Phys. B 126, 86 (2020).
  49. N. J. Stone, Table of Recommended Nuclear Magnetic Dipole Moments: Part I, Long-Lived States, INDC International Nuclear Data Committee INDC(NDS)-0794, IAEA (2019), 10.61092/iaea.yjpc-cns6.
  50. N. J. Stone, Table of Nuclear Electric Quadrupole Moments, International Nuclear Data Committee INDC(NDS)-0833, IAEA (2021), 10.61092/iaea.a6te-dg7q.
  51. D. H. Forest, R. A. Powis, E. C. A. Cochrane, J. A. R. Griffith, and G. Tungate, High resolution laser spectroscopy of naturally occurring ruthenium isotopes, J. Phys. G 41, 025106 (2014).
  52. P. Müller and W. Nörtershäuser, The qspec python package: A physics toolbox for laser spectroscopy, Comput. Phys. Commun. 311, 109550 (2025).
  53. G. Fricke and K. Heilig, Nuclear Charge Radii, in Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, Group I: Elementary Particles, Nuclei and Atoms (Springer, Berlin, Heidelberg, New York, 2004).
  54. W. H. King, Isotope Shifts in Atomic Spectra (Springer, New York, 1984).
  55. A. Papoulia, B. G. Carlsson, and J. Ekman, Effect of realistic nuclear charge distributions on isotope shifts and progress towards the extraction of higher-order nuclear radial moments, Phys. Rev. A 94, 042502 (2016).
  56. I. Kullmann, S. Goriely, O. Just, A. Bauswein, and H.-T. Janka, Impact of systematic nuclear uncertainties on composition and decay heat of dynamical and disk ejecta in compact binary mergers, Mon. Not. R. Astron. Soc. 523, 2551 (2023).
  57. S. Martinet and S. Goriely, The impact of mass uncertainties on r-process nucleosynthesis in neutron star mergers, Astron. Astrophys. 694, A180 (2025).
  58. J. Deprince, G. Wagle, S. B. Nasr, H. C. Gallego, M. Godefroid, S. Goriely, O. Just, P. Palmeri, P. Quinet, and S. V. Eck, Kilonova ejecta opacity inferred from new large-scale HFR atomic calculations in all elements between Ca (Z=20) and Lr (Z=103), Astron. Astrophys. 696, A32 (2025).
  59. S. Geldhof et al., Impact of nuclear deformation and pairing on the charge radii of palladium isotopes, Phys. Rev. Lett. 128, 152501 (2022).
  60. F. C. Charlwood et al., Nuclear charge radii of molybdenum fission fragments, Phys. Lett. B 674, 23 (2009).
  61. L. Renth et al., Nuclear moments and radii of palladium isotopes (to be published).

  62. We provide the expression for the radius of such a drop and a more in-depth analysis in the Supplemental Material [9].

  63. V. M. Strutinsky, “Shells” in deformed nuclei, Nucl. Phys. A122, 1 (1968).
  64. E. Verstraelen et al., Search for octupole-deformed actinium isotopes using resonance ionization spectroscopy, Phys. Rev. C 100, 044321 (2019).
  65. R. W. Hasse and W. D. Myers, Geometrical Relationships of Macroscopic Nuclear Physics, Springer Series in Nuclear and Particle Physics (Springer, Berlin Heidelberg, 1988).
  66. W. D. Myers and K.-H. Schmidt, An update on droplet-model charge distributions, Nucl. Phys. A410, 61 (1983).

  67. We show in the Supplemental Material [9] that this is a representative choice.

Outline

Information

Phys. Rev. Lett. 135, 202501– Published 10 November, 2025
  • Received 10 March 2025
  • Accepted 10 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation