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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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## 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.

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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

### 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.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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.

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Reprints and Permissions

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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