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Mirror-symmetry violation in bound nuclear ground states

Abstract

Conservation laws are deeply related to any symmetry present in a physical system1,2. Analogously to electrons in atoms exhibiting spin symmetries3, it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t = 1/2 (ref. 4). Every nuclear state is thus characterized by a total isobaric spin T and a projection Tz—two quantities that are largely conserved in nuclear reactions and decays5,6. A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states7, including their ground state, labelled by their total angular momentum J and parity π. Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a Jπ = 5/2 spin assignment is needed to explain the proton-emission pattern observed from the T = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its Jπ = 1/2 mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei.

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Fig. 1: Particle identification plot.
Fig. 2: Decay spectra of 73Sr β-delayed proton emission.
Fig. 3: Proposed level scheme.

Data availability

Raw data were generated at the National Superconducting Cyclotron Laboratory large-scale facility. All of the relevant data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Noether, E. Invariante Variationsprobleme. Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1918, 235–257 (1918).

    MATH  Google Scholar 

  2. Elliott, J. & Dawber, P. Symmetry in Physics: Principles and Simple Applications (Oxford Univ. Press, 1984).

  3. Dirac, P. A. M. The quantum theory of the electron. Proc. R. Soc. Lond. A 117, 610–624 (1928).

    Article  ADS  MATH  Google Scholar 

  4. Heisenberg, W. On the structure of atomic nuclei. Z. Phys. 77, 1–11 (1932).

    Article  ADS  CAS  Google Scholar 

  5. Wigner, E. On the consequences of the symmetry of the nuclear Hamiltonian on the spectroscopy of nuclei. Phys. Rev. 51, 106–119 (1937).

    Article  ADS  CAS  MATH  Google Scholar 

  6. Wilkinson, D. H. Isospin in Nuclear Physics (North Holland Pub. Co., 1970).

  7. Warner, D., Bentley, M. & Van Isacker, P. The role of isospin symmetry in collective nuclear structure. Nat. Phys. 2, 311–318 (2006).

    Article  CAS  Google Scholar 

  8. Schatz, H. et al. rp-process nucleosynthesis at extreme temperature and density conditions. Phys. Rep. 294, 167–263 (1998).

    Article  ADS  CAS  Google Scholar 

  9. Grindlay, J. et al. Discovery of intense X-ray bursts from the globular cluster NGC 6624. Astrophys. J. 205, L127–L130 (1976).

    Article  ADS  Google Scholar 

  10. Woosley, S. E. & Taam, R. E. γ-ray bursts from thermonuclear explosions on neutron stars. Nature 263, 101–103 (1976).

    Article  ADS  CAS  Google Scholar 

  11. Suzuki, H. et al. Discovery of 72Rb: a nuclear sandbank beyond the proton drip line. Phys. Rev. Lett. 119, 192503 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Rogers, A. M. et al. 69Kr β-delayed proton emission: a Trojan horse for studying states in proton-unbound 69Br. Phys. Rev. C 84, 051306 (2011).

    Article  ADS  CAS  Google Scholar 

  13. Del Santo, M. et al. β-delayed proton emission of 69Kr and the 68Se rp-process waiting point. Phys. Lett. B 738, 453–456 (2014).

    Article  ADS  CAS  Google Scholar 

  14. Schmidt, K. H. A new test for random events of an exponential distribution. Eur. Phys. J. A 8, 141–145 (2000).

    Article  ADS  CAS  Google Scholar 

  15. Batchelder, J. C. et al. Beta-delayed proton decay of 73Sr. Phys. Rev. C 48, 2593–2597 (1993).

    Article  ADS  CAS  Google Scholar 

  16. Wang, M. et al. The AME2016 atomic mass evaluation: (II). Tables, graphs and references. Chinese Phys. C 41, 030003 (2017).

    Article  ADS  CAS  Google Scholar 

  17. Singh, B., Rodriguez, J., Wong, S. & Tuli, J. Review of logft values in β decay. Nucl. Data Sheets 84, 487–563 (1998).

    Article  ADS  CAS  Google Scholar 

  18. Hagberg, E. et al. Tests of isospin mixing corrections in superallowed 0+ → 0+ β decays. Phys. Rev. Lett. 73, 396–399 (1994).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Konieczka, M., Baczyk, P. & Satuła, W. β-decay study within multireference density functional theory and beyond. Phys. Rev. C 93, 042501 (2016).

    Article  ADS  CAS  Google Scholar 

  20. Bączyk, P. et al. Isospin-symmetry breaking in masses of N Z nuclei. Phys. Lett. B 778, 178–183 (2018).

    Article  ADS  CAS  Google Scholar 

  21. Michel, N., Nazarewicz, W., Płoszajczak, M. & Vertse, T. Shell model in the complex energy plane. J. Phys. G 36, 013101 (2009).

    Article  ADS  CAS  Google Scholar 

  22. Murray, G., White, W., Willmott, J. & Entwistle, R. The decay of 73Br. Nucl. Phys. A 142, 21–34 (1970).

    Article  ADS  CAS  Google Scholar 

  23. Wörmann, B. et al. Rotational bands in 73Br: the disappearance of shape coexistence in 72Se. Z. Phys. A 322, 171–172 (1985).

    Article  ADS  Google Scholar 

  24. Heese, J. et al. Spectroscopy of high spin states in 73Br. Phys. Rev. C 36, 2409–2421 (1987).

    Article  ADS  CAS  Google Scholar 

  25. Heese, J. et al. Conversion electron and yrast state measurements in 73Br. Phys. Rev. C 41, 1553–1561 (1990).

    Article  ADS  CAS  Google Scholar 

  26. Griffiths, A. G. et al. Magnetic moments and shape coexistence in the light Br isotopes. Phys. Rev. C 46, 2228–2240 (1992).

    Article  ADS  CAS  Google Scholar 

  27. Wang, S. M., Michel, N., Nazarewicz, W. & Xu, F. R. Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates. Phys. Rev. C 96, 044307 (2017).

    Article  ADS  Google Scholar 

  28. Wang, S. M. & Nazarewicz, W. Puzzling two-proton decay of 67Kr. Phys. Rev. Lett. 120, 212502 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Berggren, T. On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes. Nucl. Phys. A 109, 265–287 (1968).

    Article  ADS  Google Scholar 

  30. Bouchez, E. et al. New shape isomer in the self-conjugate nucleus 72Kr. Phys. Rev. Lett. 90, 082502 (2003).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Gade, A. et al. Quadrupole deformation of the self-conjugate nucleus 72Kr. Phys. Rev. Lett. 95, 022502 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Iwasaki, H. et al. Evolution of collectivity in 72Kr: evidence for rapid shape transition. Phys. Rev. Lett. 112, 142502 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Rykaczewski, K. et al. Proton emitters 140Ho and 141Ho: probing the structure of unbound Nilsson orbitals. Phys. Rev. C 60, 011301 (1999).

    Article  ADS  Google Scholar 

  34. Sonzogni, A. A. et al. Fine structure in the decay of the highly deformed proton emitter 131Eu. Phys. Rev. Lett. 83, 1116–1118 (1999).

    Article  ADS  CAS  Google Scholar 

  35. Kruppa, A. T., Barmore, B., Nazarewicz, W. & Vertse, T. Fine structure in the decay of deformed proton emitters: nonadiabatic approach. Phys. Rev. Lett. 84, 4549–4552 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  36. Karny, M. et al. Shell structure beyond the proton drip line studied via proton emission from deformed 141Ho. Phys. Lett. B 664, 52–56 (2008).

    Article  ADS  CAS  Google Scholar 

  37. Miller, G. A., Opper, A. K. & Stephenson, E. J. Charge symmetry breaking and QCD. Annu. Rev. Nucl. Part. Sci. 56, 253–292 (2006).

    Article  ADS  CAS  Google Scholar 

  38. Borsanyi, S. et al. Ab initio calculation of the neutron–proton mass difference. Science 347, 1452–1455 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Alvarez, L. W. & Bloch, F. A quantitative determination of the neutron moment in absolute nuclear magnetons. Phys. Rev. 57, 111–122 (1940).

    Article  ADS  CAS  Google Scholar 

  40. Wiringa, R. B., Stoks, V. G. J. & Schiavilla, R. Accurate nucleon–nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995).

    Article  ADS  CAS  Google Scholar 

  41. Thomas, R. G. On the determination of reduced widths from the one-level dispersion formula. Phys. Rev. 81, 148–149 (1951).

    Article  ADS  CAS  Google Scholar 

  42. Ehrman, J. B. On the displacement of corresponding energy levels of 13C and 13N. Phys. Rev. 81, 412–416 (1951).

    Article  ADS  CAS  Google Scholar 

  43. Thomas, R. G. An analysis of the energy levels of the mirror nuclei, 13C and 13N. Phys. Rev. 88, 1109–1125 (1952).

    Article  ADS  CAS  Google Scholar 

  44. Morrissey, D., Sherrill, B., Steiner, M., Stolz, A. & Wiedenhoever, I. Commissioning the A1900 projectile fragment separator. Nucl. Instrum. Methods Phys. Res. B 204, 90–96 (2003).

    Article  ADS  CAS  Google Scholar 

  45. Bazin, D. et al. Radio Frequency Fragment Separator at NSCL. Nucl. Instrum. Methods Phys. Res. A 606, 314–319 (2009).

    Article  ADS  CAS  Google Scholar 

  46. Prisciandaro, J., Morton, A. & Mantica, P. Beta counting system for fast fragmentation beams. Nucl. Instrum. Methods Phys. Res. A 505, 140–143 (2003).

    Article  ADS  CAS  Google Scholar 

  47. Mueller, W. et al. Thirty-two-fold segmented germanium detectors to identify γ-rays from intermediate-energy exotic beams. Nucl. Instrum. Methods Phys. Res. A 466, 492–498 (2001).

    Article  ADS  CAS  Google Scholar 

  48. Prokop, C. et al. Digital data acquisition system implementation at the National Superconducting Cyclotron Laboratory. Nucl. Instrum. Methods Phys. Res. A 741, 163–168 (2014).

    Article  ADS  CAS  Google Scholar 

  49. Kibédi, T., Burrows, T. W., Trzhaskovskaya, M. B., Davidson, P. M. & Nestor, C. W. Jr. Evaluation of theoretical conversion coefficients using BrIcc. Nucl. Instrum. Methods Phys. Res. A 589, 202–229 (2008).

    Article  ADS  CAS  Google Scholar 

  50. Condon, E. U. & Odishaw, H. Handbook of Physics (McGraw-Hill, 1958).

  51. Hagberg, E. et al. The decay of a new nuclide: 71B. Nucl. Phys. A 383, 109–118 (1982).

    Article  ADS  Google Scholar 

  52. Meisel, Z. et al. β-particle energy-summing correction for β-delayed proton emission measurements. Nucl. Instrum. Methods Phys. Res. A 844, 45–52 (2017).

    Article  ADS  CAS  Google Scholar 

  53. Huang, W. J. & Audi, G. Corrections of alpha- and proton-decay energies in implantation experiments. EPJ Web Conf. 146, 10007 (2017).

    Article  CAS  Google Scholar 

  54. International Network of Nuclear Structure and Decay Data Evaluators. Evaluated nuclear structure data file (ENSDF) National Nuclear Data Center (Brookhaven National Laboratory, 2020); https://www.nndc.bnl.gov/ensdf/.

  55. Cwiok, S., Nazarewicz, W., Dudek, J., Skalski, J. & Werner, T. Single-particle energies, wave functions, quadrupole moments and g-factors in an axially deformed Woods−Saxon potential with applications to the two-centre-type nuclear problems. Comput. Phys. Commun. 46, 379–399 (1987).

    Article  ADS  CAS  Google Scholar 

  56. Nazarewicz, W., Dudek, J., Bengtsson, R., Bengtsson, T. & Ragnarsson, I. Microscopic study of the high-spin behaviour in selected A 80 nuclei. Nucl. Phys. A 435, 397–447 (1985).

    Article  ADS  Google Scholar 

  57. Thompson, I. J. et al. Pauli blocking in three-body models of halo nuclei. Phys. Rev. C 61, 024318 (2000).

    Article  ADS  Google Scholar 

  58. Thompson, I. J., Nunes, F. M. & Danilin, B. V. FaCE: a tool for three body Faddeev calculations with core excitation. Comput. Phys. Commun. 161, 87–107 (2004); erratum 170, 296–297 (2005).

    Article  ADS  CAS  MATH  Google Scholar 

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Acknowledgements

We would like to thank T. Ginter for his effort in providing the 73Sr beam used in the experiment. We acknowledge support from the US DOE, Office of Science, Office of Nuclear Physics under award numbers DE-FG02-94ER40848 (UML), DE-AC02-06CH11357 (ANL), DE-SC0013365 and DE-SC0018083 (FRIB), as well as DE-FG02-88ER40387 and DE-SC0019042 (OU); the NNSA through award numbers DE-NA0003180 (NSSC), DE-NA0000979 (NSSC), DE-NA0003221, DE-NA0003909 and/or DE-NA0002132; and the NSF under contract numbers PHY-1-102511 and PHY 14-30152.

Author information

Authors and Affiliations

Authors

Contributions

D.E.M.H. performed the offline analysis and prepared the figures as well as the writing for the manuscript. A.M.R. was the principle investigator of the 73Sr experiment, was responsible for preparing and executing the measurement with C.M., and aided in writing and preparing the manuscript. S.M.W. performed the GCC calculations, prepared tables and prepared the text for these aspects of the manuscript. C.J.L. and W.N. aided in writing and preparing the manuscript. C.M. led the experimental preparations and oversaw conducting the measurement. S.N.L. assisted in the design, setup, and execution of the experiment. P.C.B., K.B., K.C., J.A.C., A.C.D., E.R.D., S.J., R.L., Z.M., H.S., K.S., D.S. and S.K.S. assisted in setting up the experiment and/or checked the data accumulation online and maintained operation of the experiment. S.W. aided in the offline analysis.

Corresponding authors

Correspondence to D. E. M. Hoff or A. M. Rogers.

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The authors declare no competing interests.

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Peer review information Nature thanks Bertram Blank and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Time between implantation of 73Sr and first decay event with logarithmic bins.

The first decay events found after implantation are plotted with logarithmic bins. The resulting maximum logarithmic likelihood fit to the data is shown as the solid red curve. The horizontal error bars correspond to the bin size, and the vertical error bars correspond to one standard deviation from counting.

Extended Data Fig. 2 The mirror chart of nuclides.

Mirror nuclei are plotted according to the isobaric spin (T) of their ground-state configurations. For almost the entire mirror chart, the spin and parity, Jπ, of the ground states are identically reflected across the N = Z line54. The black squares with cracks show the only two places on the mirror chart where this ground-state mirror symmetry is known or believed to be broken. Once adjusting for the energy shift of levels due to charge-breaking forces, the relative masses (ΔM) of mirror pairs (with the same magnitude Tz) become comparable, and the connection to IASs in neighbouring nuclei becomes clearer. This is illustrated by the isobar diagrams comparing the relative masses for two T = 3/2 multiplets, one in the A = 9 system and the other in the A = 73 system of interest.

Extended Data Table 1 GCC analysis
Extended Data Table 2 Predicted spectra of 73Sr and 73Br

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Hoff, D.E.M., Rogers, A.M., Wang, S.M. et al. Mirror-symmetry violation in bound nuclear ground states. Nature 580, 52–55 (2020). https://doi.org/10.1038/s41586-020-2123-1

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