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Nuclear moments of indium isotopes reveal abrupt change at magic number 82

Abstract

In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular ‘magic’ numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics3,4,5. The indium isotopes are considered a textbook example of this phenomenon6, in which the constancy of their electromagnetic properties indicated that a single unpaired proton hole can provide the identity of a complex many-nucleon system6,7. Here we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 indicates that, whereas the single-particle picture indeed dominates at neutron magic number N = 82 (refs. 2,8), it does not for previously studied isotopes. To investigate the microscopic origin of these observations, our work provides a combined effort with developments in two complementary nuclear many-body methods: ab initio valence-space in-medium similarity renormalization group and density functional theory (DFT). We find that the inclusion of time-symmetry-breaking mean fields is essential for a correct description of nuclear magnetic properties, which were previously poorly constrained. These experimental and theoretical findings are key to understanding how seemingly simple single-particle phenomena naturally emerge from complex interactions among protons and neutrons.

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Fig. 1: Evolution of nuclear electromagnetic properties for the 9/2+ ground states of 105–131 In isotopes.
Fig. 2: A breakdown of the contributions of the polarized core states.
Fig. 3: Nuclear magnetic moments for the 1/2 isomeric states of 113–131In isotopes.

Data availability

Examples of spectra source data for the previously unmeasured 129,131In isotopes, most relevant to this work, are included in this article. The full datasets generated and/or analysed during the current study are available in the Zenodo repository, https://doi.org/10.5281/zenodo.6406949. The code used to analyse the data is also included in the repository.

The data files related to the DFT calculations are available at https://webfiles.york.ac.uk/HFODD/Projects/Magnetic_and_electric_moments_in_Indium/.

Code availability

The code used to analyse the data is included in the Zenodo repository, https://doi.org/10.5281/zenodo.6406949.

The code used to perform the DFT calculations is available at https://webfiles.york.ac.uk/HFODD/Projects/hf301m/.

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Acknowledgements

This work was supported by ERC Consolidator Grant no. 648381 (FNPMLS); STFC grants ST/L005794/1, ST/L005786/1, ST/P004423/1, ST/M006433/1 and ST/P003885/1, and Ernest Rutherford grant no. ST/L002868/1; the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under grant DE-SC0021176; GOA 15/010 from KU Leuven, BriX Research Program No. P7/12; the FWO-Vlaanderen (Belgium); the European Unions Grant Agreement 654002 (ENSAR2); National Key R&D Program of China (contract no. 2018YFA0404403); the National Natural Science Foundation of China (no. 11875073); the Polish National Science Centre under contract no. 2018/31/B/ST2/02220. TRIUMF receives funding by a contribution through the National Research Council of Canada. The theoretical work was further supported by NSERC and the U.S. Department of Energy under contract DE-FG02-97ER41014. The VS-IMSRG computations were performed with an allocation of computing resources on Cedar at WestGrid and Compute Canada, and on the Oak Cluster at TRIUMF managed by the University of British Columbia department of Advanced Research Computing (ARC). We would also like to thank the ISOLDE technical group for their support and assistance and the University of Jyväskylä for the use of the injection-locked cavity. We acknowledge the CSC – IT Center for Science Ltd., Finland, for the allocation of computational resources. This project was partly undertaken on the Viking Cluster, which is a high-performance computing facility provided by the University of York. We are grateful for computational support from the University of York High Performance Computing service, Viking and the Research Computing team.

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Contributions

A.R.V. prepared the manuscript with input from all authors, especially R.F.G.R., J.Bo., J.D., J.D.H., T.M., G.N., K.T.F., T.E.C., R.P.deG. and S.R.S. R.F.G.R., J.Bi., C.L.B., M.L.B., T.E.C., K.T.F., W.G., R.P.deG., A.K., K.M.L., G.N., S.G.W., A.R.V. and X.F.Y. proposed the experiment(s), A.R.V., C.L.B., M.L.B., T.E.C., K.T.F., G.J.F.-S., G.G., W.G., R.P.deG., R.H., A.K., D.L., K.M.L., R.F.G.R., S.G.W., X.F.Y. and D.Y. conducted the experiment(s), A.R.V., C.L.B., R.F.G.R. and J.H. analysed the results, J.Bo. and J.D. performed theoretical (DFT) nuclear calculations, J.D.H., T.M. and S.R.S. performed theoretical (VS-IMSRG) nuclear calculations. All authors reviewed the manuscript.

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Correspondence to A. R. Vernon or R. F. Garcia Ruiz.

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Extended data figures and tables

Extended Data Fig. 1 Example hyperfine spectra of the 129In and 131In isotopes.

a, b, Example spectra measured using the 246.8-nm (5p 2P3/2 → 9s 2S1/2) transition (a), and using the 246.0-nm (5p 2P1/2 → 8s 2S1/2) transition (b). The 9/2+ ground and 1/2 isomer states are indicated.

Extended Data Table 1 The Bhf hyperfine structure parameter (from the 2P3/2 state) values, measured in this work for the odd-mass 113–131In isotopes and the extracted electric quadrupole moment values

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Vernon, A.R., Garcia Ruiz, R.F., Miyagi, T. et al. Nuclear moments of indium isotopes reveal abrupt change at magic number 82. Nature 607, 260–265 (2022). https://doi.org/10.1038/s41586-022-04818-7

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