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78Ni revealed as a doubly magic stronghold against nuclear deformation


Nuclear magic numbers correspond to fully occupied energy shells of protons or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. Although the sequence of magic numbers is well established for stable nuclei, experimental evidence has revealed modifications for nuclei with a large asymmetry between proton and neutron numbers. Here we provide a spectroscopic study of the doubly magic nucleus 78Ni, which contains fourteen neutrons more than the heaviest stable nickel isotope. We provide direct evidence of its doubly magic nature, which is also predicted by ab initio calculations based on chiral effective-field theory interactions and the quasi-particle random-phase approximation. Our results also indicate the breakdown of the neutron magic number 50 and proton magic number 28 beyond this stronghold, caused by a competing deformed structure. State-of-the-art phenomenological shell-model calculations reproduce this shape coexistence, predicting a rapid transition from spherical to deformed ground states, with 78Ni as the turning point.

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We thank the staff of the RIKEN Nishina Center accelerator complex for providing a stable and high-intensity uranium beam and the BigRIPS team for the smooth operation of the secondary beams. We also thank N. Miyauchi for 3D schematic of the RIBF facility shown in Fig. 2a. The development of MINOS and the core MINOS team have been supported by the European Research Council through ERC grant number MINOS-258567. R.T. was supported by JSPS Grant-in-Aid for JSPS Research Fellows JP14J08717. A.O. was supported by JSPS long-term fellowship L-13520 at the RIKEN Nishina Center. C. Santamaria was supported by the IPA programme at the RIKEN Nishina Center. J.D.H. acknowledges support by the National Research Council of Canada and NSERC. This work was supported in part by the ERC through grant number 307986 STRONGINT, the DFG under grant SFB 1245 and the BMBF under contract number 05P18RDFN1. The MCSM calculations were performed on the K computer at RIKEN AICS (hp160211, hp170230, hp180179). J.M., T.O. and Y.T. acknowledge support from MEXT as ‘Priority Issue on post-K computer’ (Elucidation of the Fundamental Laws and Evolution of the Universe) and JICFuS. J.M. and K.O. were supported by Grant-in-Aid for Scientific Research JP18K03639 (J.M.) and JP16K05352 (K.O.). A. Poves acknowledges support by Mineco (Spain) grants FPA2014-57916 and Severo Ochoa Program SEV-2016-0597. This work was supported in part by the DFG through the Cluster of Excellence PRISMA. L.X.C. was supported by Vietnam MOST through the Physics Development Program grant TLCN.25/18. Z.D., Z.K. and Z.V. acknowledge support from the GINOP-2.3.3-15-2016-00034 project. M.L, C.L and V.W. acknowledge support from the German BMBF through grants 05P15RDNF1 and 05P12RDNF8.

Author information

R.T. performed offline data analyses and GEANT4 simulations and prepared the figures; P.D. and A.O. designed the experiment; R.T., C. Santamaria, P.D., A.O., J.D.H., J.M., F.N., K.O., T.O., A.S. and Y.T. wrote the manuscript; R.T., C. Santamaria, P.D., A.O., G.A., D.C., F.C., A.C., A.D., J.-M.G., A.G., V.L., M.M., S.M., M.N., C.P., A. Peyaud, E.C.P., J.-Y.R., Y.S., S.T. and H.W. were responsible for setting up the liquid-hydrogen target, the vertex reconstruction system, MINOS and the γ-ray detector array, DALI2; R.T., C. Santamaria, H.B., D.C., A.C. and T.I. were responsible for the data acquisition system and analysis software; R.T., C. Santamaria, P.D., A.O., G.A., H.B., D.C., F.C., A.C., A.D., J.-M.G., A.G., T.I., V.L., M.M., S.M., M.N., H.O., C.P., A. Peyaud, E.C.P., J.-Y.R., Y.S., S.T., H.W., F.B., L.X.C., Z.D., S.F., F.G., A.G., K.H., Z.K., S.K., J.L., M.L., C.L., R.L., K.N., T. Miyazaki, S.N., L.O., S.O., Z.P., E.S., C. Shand, P.-A.S., I.S., D. Steppenbeck, T.S., D. Suzuki, Z.V., V.W., J.W. and Z.Y.X. checked the data accumulation online and maintained operation of the experiment; P.D., A.O., K.Y., T. Motobayashi, H.S. and T.U. supervised the participants; F.N. and A. Poves performed the LSSM calculations; T.O. and Y.T. performed the MCSM calculations; S.P. performed the QRPA calculations; J.D.H., J.M., A.S., J.S. and S.R.S. performed the IM-SRG calculations; K.O. performed the DWIA calculations. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to P. Doornenbal.

Extended data figures and tables

  1. Extended Data Fig. 1 Energy spectra of prompt γ-ray coincidences with 79Cu(p, 2p)78Ni reactions.

    a, As in Fig. 3a, but with a binning of 40 keV, which allows us to resolve the transition at 583 keV. b, γ-ray spectrum in coincidence with the 583-keV transition. The expected intensities for coincidences with the 583-keV transition are indicated by the simulated lineshapes with and without the 1,103-keV transition, shown by the blue dashed and magenta solid lines, respectively. The results reveal no coincidence between the 583- and 1,103-keV transitions. c, γ-ray spectrum in coincidence with the 1,103-keV transition. The hypothesis of no coincidence between the 583- and 1,103-keV transitions is corroborated. Coincidence ranges are illustrated by the shaded areas in b and c.

  2. Extended Data Fig. 2 Evolution of peak significance and fitted intensities as a function of γ-ray multiplicity.

    a, b, Number of emitted γ-rays obtained for the fitted individual transitions. c, d, S.L. of individual transitions for the 79Cu(p, 2p)78Ni (c) and 80Zn(p, 3p)78Ni (d) reactions.

  3. Extended Data Table 1 Observed γ-ray transition energies, relative intensities and S.L. for the 79Cu(p, 2p)78Ni and 80Zn(p, 3p)78Ni reaction channels

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Fig. 1: Experimental \({\boldsymbol{E}}({{\rm{2}}}_{{\rm{1}}}^{{\rm{+}}})\) systematics of the even–even nuclear landscape.
Fig. 2: Layout of the experimental equipment and particle identification plots of isotopes.
Fig. 3: Doppler-corrected γ-ray energy spectra.
Fig. 4: Comparison of theoretical predictions with experimental data.
Fig. 5: Experimental and calculated partial cross-sections for the 79Cu(p, 2p)78Ni reaction.
Extended Data Fig. 1: Energy spectra of prompt γ-ray coincidences with 79Cu(p, 2p)78Ni reactions.
Extended Data Fig. 2: Evolution of peak significance and fitted intensities as a function of γ-ray multiplicity.


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