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# Precision mass measurement of lightweight self-conjugate nucleus 80Zr

## Abstract

Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. The nuclear shell structure varies as a result of changes in the nuclear mean field with the number of neutrons N and protons Z, and these variations can be probed by measuring the mass differences between nuclei. The N = Z = 40 self-conjugate nucleus 80Zr is of particular interest, as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. Here we provide evidence for the existence of a deformed double-shell closure in 80Zr through high-precision Penning trap mass measurements of 80–83Zr. Our mass values show that 80Zr is substantially lighter, and thus more strongly bound than predicted. This can be attributed to the deformed shell closure at N = Z = 40 and the large Wigner energy. A statistical Bayesian-model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

## Code availability

Our unpublished computer codes used to generate the results reported in this paper and central to its main claims will be made available upon request.

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## Acknowledgements

We thank the NSCL staff for their technical support as well as R. F. Casten for useful discussions on interpreting the results of the experiment. This work was conducted with the support of Michigan State University, the US National Science Foundation under contracts nos. PHY-1565546 (A.H., E.L., R.J., G.B., K.L., C.R.N., D.P., R.R., C.S.S. and I.T.Y.), PHY-1913554 (R.J.) and PHY-1430152 (R.J.), the US Department of Energy, Office of Science, Office of Nuclear Physics under awards nos. DE-SC0013365 (W.N. and L.N.) and DE-SC0018083 (NUCLEI SciDAC-4 collaboration) (S.A.G. and W.N.) and by the National Science Foundation CSSI programme under award no. 2004601 (BAND collaboration; W.N.).

## Author information

Authors

### Contributions

A.H., E.L., G.B., K.L., C.R.N., D.P., R.R., C.S.S. and I.T.Y. performed the experiment. A.H., E.L., D.P. and I.T.Y. performed the data analysis. A.H., E.L., W.N., S.A.G. and L.N. prepared the manuscript. R.J., S.A.G., W.N. and L.N. performed the Bayesian analysis. All authors discussed the results and provided comments on the manuscript.

### Corresponding author

Correspondence to A. Hamaker.

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### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Alessandro Pastore, Anu Kankainen and Bo Cederwall for their contribution to the peer review of this work.

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Hamaker, A., Leistenschneider, E., Jain, R. et al. Precision mass measurement of lightweight self-conjugate nucleus 80Zr. Nat. Phys. 17, 1408–1412 (2021). https://doi.org/10.1038/s41567-021-01395-w

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