Abstract
In rare cases, the removal of a single proton (Z) or neutron (N) from an atomic nucleus leads to a dramatic shape change. These instances are crucial for understanding the components of the nuclear interactions that drive deformation. The mercury isotopes (Z = 80) are a striking example1,2: their close neighbours, the lead isotopes (Z = 82), are spherical and steadily shrink with decreasing N. The even-mass (A = N + Z) mercury isotopes follow this trend. The odd-mass mercury isotopes 181,183,185Hg, however, exhibit noticeably larger charge radii. Due to the experimental difficulties of probing extremely neutron-deficient systems, and the computational complexity of modelling such heavy nuclides, the microscopic origin of this unique shape staggering has remained unclear. Here, by applying resonance ionization spectroscopy, mass spectrometry and nuclear spectroscopy as far as 177Hg, we determine 181Hg as the shape-staggering endpoint. By combining our experimental measurements with Monte Carlo shell model calculations, we conclude that this phenomenon results from the interplay between monopole and quadrupole interactions driving a quantum phase transition, for which we identify the participating orbitals. Although shape staggering in the mercury isotopes is a unique and localized feature in the nuclear chart, it nicely illustrates the concurrence of single-particle and collective degrees of freedom at play in atomic nuclei.
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Data availability
All of the relevant data that support the findings of this study are available from the corresponding author upon reasonable request.
Change history
24 January 2022
A Correction to this paper has been published: https://doi.org/10.1038/s41567-022-01503-4
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Acknowledgements
This work has received funding through the following channels: the Max-Planck-Society, IMPRS-PTFS; BMBF (German Federal Ministry for Education and Research) Nos. 05P12HGCI1 and 05P15HGCIA; STFC Grant Nos. ST/L005727, ST/M006433, ST/M006434, ST/L002868/1, ST/L005794/1; Slovak Research and Development Agency, contract No. APVV-14-0524; European Unions Seventh Framework Programme for Research and Technological Development under Grant Agreements 267194 (COFUND) and 289191 (LA3NET). FWO-Vlaanderen (Belgium), by GOA/2015/010 (BOF KU Leuven); the Inter-university Attraction Poles Programme initiated by the Belgian Science Policy Office (BriX network P7/12), by the European Commission within the Seventh Framework Programme through I3-ENSAR (contract no. RII3-CT-2010-262010) and by a grant from the European Research Council (ERC-2011-AdG-291561-HELIOS). S.S acknowledges the Agency for Innovation by Science and Technology in Flanders (IWT). L.P.G acknowledges FWO-Vlaanderen (Belgium) as an FWO Pegasus Marie Curie Fellow. A.W and K.Z acknowledge the Wolfgang-Gentner scholarship and the BMBF (German Federal Ministry for Education and Research) no. 05P12ODCIA. This work was supported by JSPS and FWO under the Japan-Belgium Research Cooperative Program. The MCSM calculations were performed on the K computer at RIKEN AICS (hp160211, hp170230). This work was also supported in part by Priority Issue on Post-K computer (Elucidation of the Fundamental Laws and Evolution of the Universe) from MEXT and JICFuS. J.D. and A.P. acknowledge partial support from the STFC grant No. ST/P003885/1. The density functional theory calculations were performed using the DiRAC Data Analytic system at the University of Cambridge, operated by the University of Cambridge High Performance Computing Service on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations grant ST/K00333X/1. DiRAC is part of the National e-Infrastructure.
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A.N.A, A.E.B, T.D.G, D.V.F, V.N.F, L.P.G, M.H, B.A.M, M.D.S. and P.V.D. conceived the experiment and prepared the proposal; T.D.G, D.V.F, V.N.F, B.A.M, Y.M.P, P.L.M, R.E.R, S.R. and M.V. carried out laser ionization scheme and/or ion source developments; A.N.A, K.B, T.E.C, V.N.F, M.H, S.K, B.A.M, L.S, P.V.D. and K.Z. supervised the participants; B.A, N.A.A, D.A, A.E.B, J.B, T.E.C, J.G.C, T.D.G, G.J.F.-S., D.V.F, V.N.F, K.T.F, L.P.G, L.G, M.H, K.M.L, V.M, B.A.M, Y.M.P, P.L.M, R.E.R, S.S, P.S, C.V.B, P.V.D, M.V, E.V, A.W, F.W. and A.Z. participated in data taking; T.O. and Y.T. performed MCSM calculations; J.D. and A.P. performed density functional theory calculations; A.E.B, T.D.G, D.V.F, B.A.M, P.L.M, R.E.R, S.R. and M.V. took part in laser set-up and operation; B.A, D.A, T.E.C, J.G.C, K.T.F, L.P.G, L.G, K.M.L, V.M, M.R, R.E.R, L.S, S.S, C.V.B, A.W, F.W. and R.N.W. set up and operated the detection and data acquisition systems; A.N.A, A.E.B, K.B, T.E.C, T.D.G, J.D, D.V.F, L.P.G, M.H, B.A.M, T.O, L.S, M.D.S, S.S, P.V.D, E.V. and K.W. contributed to the data analysis and interpretation; A.N.A, A.E.B, K.B, T.E.C, J.G.C, T.D.G, J.D, V.N.F, L.P.G, M.H, D.L, B.A.M, T.O, L.S, S.S, Y.T. and P.V.D. contributed to the manuscript preparation.
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Marsh, B.A., Day Goodacre, T., Sels, S. et al. Characterization of the shape-staggering effect in mercury nuclei. Nature Phys 14, 1163–1167 (2018). https://doi.org/10.1038/s41567-018-0292-8
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DOI: https://doi.org/10.1038/s41567-018-0292-8
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