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Oscillating Nuclear Charge Radii as Sensors for Ultralight Dark Matter

Abhishek Banerjee1,*, Dmitry Budker2,3,4, Melina Filzinger5, Nils Huntemann5,†, Gil Paz6, Gilad Perez1, Sergey Porsev7, and Marianna Safronova7,8

  • *Contact author: abhishek.banerjee@weizmann.ac.il
  • †Contact author: nils.huntemann@ptb.de
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Phys. Rev. Lett. 135, 223001 – Published 24 November, 2025

DOI: https://doi.org/10.1103/37vw-gc1r

Abstract

We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamic (QCD) axion and scalar dark matter, an effect which is of particular importance for heavy elements. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the S21/2(F=0)↔F27/2(F=3) electric octupole and S21/2(F=0)↔D23/2(F=2) electric quadrupole transitions in Yb+171. Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped Yb+171 ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements.

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References (95)

  1. J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. 120B, 127 (1983).
  2. L. F. Abbott and P. Sikivie, Phys. Lett. 120B, 133 (1983).
  3. M. Dine and W. Fischler, Phys. Lett. 120B, 137 (1983).
  4. A. Hook, Proc. Sci. TASI2018 (2019) 004 [arXiv:1812.02669].
  5. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, Phys. Rep. 870, 1 (2020).
  6. A. Arvanitaki, J. Huang, and K. Van Tilburg, Phys. Rev. D 91, 015015 (2015).
  7. A. Banerjee, H. Kim, and G. Perez, Phys. Rev. D 100, 115026 (2019).
  8. A. Chatrchyan and G. Servant, J. Cosmol. Astropart. Phys. 06 (2023) 036.
  9. F. Piazza and M. Pospelov, Phys. Rev. D 82, 043533 (2010).
  10. H. Kim and G. Perez, Phys. Rev. D 109, 015005 (2024).
  11. D. Antypas et al., arXiv:2203.14915.
  12. A. Hees, J. Guéna, M. Abgrall, S. Bize, and P. Wolf, Phys. Rev. Lett. 117, 061301 (2016).
  13. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Phys. Rev. Lett. 125, 201302 (2020).
  14. T. Kobayashi, A. Takamizawa, D. Akamatsu, A. Kawasaki, A. Nishiyama, K. Hosaka, Y. Hisai, M. Wada, H. Inaba, T. Tanabe, and M. Yasuda, Phys. Rev. Lett. 129, 241301 (2022).
  15. V. V. Flambaum and E. V. Shuryak, Phys. Rev. D 65, 103503 (2002).
  16. X. Zhang, A. Banerjee, M. Leyser, G. Perez, S. Schiller, D. Budker, and D. Antypas, Phys. Rev. Lett. 130, 251002 (2023).
  17. R. Oswald et al., Phys. Rev. Lett. 129, 031302 (2022).
  18. K. Krane, Introductory Nuclear Physics (Wiley, New York, 1991).
  19. W. King, Isotope Shifts in Atomic Spectra, Physics of Atoms and Molecules (Springer, New York, 2013).

  20. This discussion can be extended to transitions in two different atomic species when allowing for two different charge radii.

  21. J. L. Friar and J. W. Negele, Theoretical and experimental determination of nuclear charge distributions, in Advances in Nuclear Physics: Volume 8, edited by M. Baranger and E. Vogt (Springer, Boston, MA, 1975), pp. 219–376.
  22. J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Phys. Rev. C 96, 014303 (2017).
  23. A. W. Thomas, S. Theberge, and G. A. Miller, Phys. Rev. D 24, 216 (1981).
  24. E. Epelbaum, H.-W. Hammer, and U.-G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).
  25. M. Vanderhaeghen and T. Walcher, Nucl. Phys. News 21, 14 (2011).
  26. N. B. Mandache and D. I. Palade, J. Mod. Phys. 09, 1459 (2018).
  27. N. Ishii, S. Aoki, and T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007).
  28. C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. C 53, 2086 (1996).
  29. C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994).
  30. P. G. Reinhard, Rep. Prog. Phys. 52, 439 (1989).
  31. P. Ring, Prog. Part. Nucl. Phys. 37, 193 (1996).
  32. Y. K. Gambhir, P. Ring, and A. Thimet, Ann. Phys. (N.Y.) 198, 132 (1990).
  33. A. Pich, Rep. Prog. Phys. 58, 563 (1995).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/37vw-gc1r for a detailed derivation of the numerical values for the parameters α and β used in the analysis and an order-of-magnitude estimate of the field shift coefficient, which includes Refs. [35–53].
  35. J.-W. Chen, G. Rupak, and M. J. Savage, Nucl. Phys. A653, 386 (1999).
  36. T. Niksic, D. Vretenar, and P. Ring, Prog. Part. Nucl. Phys. 66, 519 (2011).
  37. J. D. Walecka, Ann. Phys. (N.Y.) 83, 491 (1974).
  38. C. J. Horowitz and B. D. Serot, Nucl. Phys. A368, 503 (1981).
  39. L. D. Miller and A. E. S. Green, Phys. Rev. C 5, 241 (1972).
  40. R. Brockmann, Phys. Rev. C 18, 1510 (1978).
  41. R. J. Furnstahl and B. D. Serot, Nucl. Phys. A468, 539 (1987).
  42. M. Neubert, Phys. Rep. 245, 259 (1994).
  43. A. V. Manohar, Phys. Rev. D 56, 230 (1997).
  44. J. L. Friar, Ann. Phys. (N.Y.) 122, 151 (1979).
  45. R. Baltin, Z. Naturforsch. 40A, 379 (1985).
  46. R. Zwicky, Phys. Rev. D 110, 014048 (2024).
  47. K. Hashimoto, K. Ohashi, and T. Sumimoto, Phys. Rev. D 105, 106008 (2022).
  48. J. R. Pelaez and G. Rios, Phys. Rev. Lett. 97, 242002 (2006).
  49. R. J. Hill and G. Paz, Phys. Rev. D 95, 094017 (2017).
  50. D. Lee, U.-G. Meißner, K. A. Olive, M. Shifman, and T. Vonk, Phys. Rev. Res. 2, 033392 (2020).
  51. N. R. Acharya, F.-K. Guo, M. Mai, and U.-G. Meißner, Phys. Rev. D 92, 054023 (2015).
  52. P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  53. Dmitry Budker and Derek Kimball, and David DeMille, Atomic physics (Second Edition) (Oxford University Press, New York, 2008).
  54. A. Banerjee, G. Paz, and G. Perez (to be published).

  55. Our discussions can be extended for a more general ultralight scalar DM couplings with the SM QCD sector, and also to extend it to include the couplings to the quarks.

  56. L. Ubaldi, Phys. Rev. D 81, 025011 (2010).
  57. R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977).
  58. R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
  59. S. Weinberg, Phys. Rev. Lett. 40, 223 (1978).
  60. F. Wilczek, Phys. Rev. Lett. 40, 279 (1978).
  61. J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
  62. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B166, 493 (1980).
  63. A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980).
  64. M. Dine, W. Fischler, and M. Srednicki, Phys. Lett. 104B, 199 (1981).
  65. P. Di Vecchia and G. Veneziano, Nucl. Phys. B171, 253 (1980).

  66. As mentioned in [10, 56], the nucleon mass also depends on the pion mass, so any variation in the pion mass would also lead to a variation in the nucleon mass as Δmnucleonmnucleon=0.06Δmπ2mπ2.(16)

  67. M. G. Kozlov and V. A. Korol, Notes on volume shift (in Russian), 10.13140/RG.2.2.28084.31361.
  68. V. A. Korol and M. G. Kozlov, Phys. Rev. A 76, 022103 (2007).
  69. M. S. Safronova, S. G. Porsev, M. G. Kozlov, J. Thielking, M. V. Okhapkin, P. Glowacki, D. M. Meier, and E. Peik, Phys. Rev. Lett. 121, 213001 (2018).
  70. M. G. Kozlov, S. G. Porsev, and V. V. Flambaum, J. Phys. B 29, 689 (1996).
  71. M. G. Kozlov, S. G. Porsev, M. S. Safronova, and I. I. Tupitsyn, Comput. Phys. Commun. 195, 199 (2015).
  72. J. Hur, D. P. L. Aude Craik, I. Counts, E. Knyazev, L. Caldwell, C. Leung, S. Pandey, J. C. Berengut, A. Geddes, W. Nazarewicz, P.-G. Reinhard, A. Kawasaki, H. Jeon, W. Jhe, and V. Vuletić, Phys. Rev. Lett. 128, 163201 (2022).
  73. I. Angeli and K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
  74. N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, and E. Peik, Phys. Rev. Lett. 116, 063001 (2016).
  75. C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, Nature (London) 567, 204 (2019).
  76. R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, Phys. Rev. Lett. 126, 011102 (2021).
  77. M. Filzinger, S. Dörscher, R. Lange, J. Klose, M. Steinel, E. Benkler, E. Peik, C. Lisdat, and N. Huntemann, Phys. Rev. Lett. 130, 253001 (2023).
  78. D. Budker, J. Eby, M. Gorghetto, M. Jiang, and G. Perez, J. Cosmol. Astropart. Phys. 12 (2023) 021.
  79. J. Arakawa, J. Eby, M. S. Safronova, V. Takhistov, and M. H. Zaheer, Phys. Rev. D 110, 075007 (2024).
  80. M. Vogelsberger and S. D. M. White, Mon. Not. R. Astron. Soc. 413, 1419 (2011).
  81. R. K. Leane and J. Smirnov, J. Cosmol. Astropart. Phys. 10 (2023) 057.
  82. G. Prézeau, Astrophys. J. 814, 122 (2015).
  83. Y. Sofue, Galaxies 8, 42 (2020).
  84. G. P. Centers, J. W. Blanchard, J. Conrad, N. L. Figueroa, A. Garcon, A. V. Gramolin, D. F. Kimball, M. Lawson, B. Pelssers, J. A. Smiga, A. O. Sushkov, A. Wickenbrock, D. Budker, and A. Derevianko, Nat. Commun. 12, 1 (2021).
  85. A. Banerjee, G. Perez, M. Safronova, I. Savoray, and A. Shalit, J. High Energy Phys. 10 (2023) 042.
  86. C. Abel et al., Phys. Rev. X 7, 041034 (2017).
  87. S. Aharony, N. Akerman, R. Ozeri, G. Perez, I. Savoray, and R. Shaniv, Phys. Rev. D 103, 075017 (2021).
  88. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Phys. Rev. Lett. 125, 201302 (2020).
  89. A. Hook and J. Huang, J. High Energy Phys. 06 (2018) 036.
  90. O. Tretiak, X. Zhang, N. Figueroa, D. Antypas, A. Brogna, A. Banerjee, G. Perez, and D. Budker, Phys. Rev. Lett. 129, 031301 (2022).
  91. R. Oswald et al., Phys. Rev. Lett. 129, 031302 (2022).
  92. P. Touboul et al. (MICROSCOPE Collaboration), Phys. Rev. Lett. 129, 121102 (2022).
  93. E. Fischbach and C. Talmadge, in 31st Rencontres de Moriond: Dark Matter and Cosmology, Quantum Measurements and Experimental Gravitation (1996), pp. 443–451.
  94. M. G. Kozlov, M. S. Safronova, J. R. Crespo López-Urrutia, and P. O. Schmidt, Rev. Mod. Phys. 90, 045005 (2018).
  95. N.-H. Rehbehn, M. K. Rosner, H. Bekker, J. C. Berengut, P. O. Schmidt, S. A. King, P. Micke, M. F. Gu, R. Müller, A. Surzhykov, and J. R. C. López-Urrutia, Phys. Rev. A 103, L040801 (2021).

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Phys. Rev. Lett. 135, 223001– Published 24 November, 2025
  • Received 27 January 2023
  • Accepted 24 October 2025
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