Lightweight self-conjugate nucleus $^{80}$Zr

A. Hamaker1,2,3∗, E. Leistenschneider1,2,†, R. Jain, G. Bollen, S.A. Giuliani, K. Lund, W. Nazarewicz, L. Neufcourt, C. Nicoloff, D. Puentes, R. Ringle, C.S. Sumithrarachchi, I.T. Yandow Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA. National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA. Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA. European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT-FBK), Trento, Italy. Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom. ∗Corresponding author: hamaker@nscl.msu.edu †Current address: CERN, Geneva, Switzerland. Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. Nuclear shell structure varies across the nuclear landscape due to changes of the nuclear mean field with the number of neutrons N and protons Z. These variations can be probed with mass differences. The N=Z=40 selfconjugate nucleus Zr is of particular interest as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. In this work, we provide evidence for the existence of a deformed double shell closure in Zr through high precision Penning trap mass measurements of Zr. Our new mass values show that Zr is significantly lighter, and thus more bound than previously determined. This can be attributed to the deformed shell closure at N=Z=40 and the large Wigner energy. Our statistical Bayesian model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory. Understanding the mechanisms of structural evolution, especially for exotic nuclei far from the beta stability line, is a major challenge in nuclear science. In this context, a rich territory for studies of basic nuclear concepts is the neutron-deficient region around mass number A = 80. The nuclei in this region rapidly change their properties with proton and neutron numbers. Indeed, some of these nuclei are among the most deformed in the nuclear chart and exhibit collective behaviour, while others show noncollective excitation patterns characteristic of spherical systems. The appearance of strongly deformed configurations around Zr has been attributed to the population of the intruder g9/2 orbitals separated by the spherical N = Z = 40 subshell closure from the upper-pf shell. This particular shell structure results in coexisting configurations of different shapes predicted by theory. In particular, for the nucleus Zr, spherical and deformed (prolate, oblate, and triaxial) structures are expected to coexist at low energies, and their competition strongly depends on the size of the calculated spherical N = Z = 40 gap. Experimentally, Zr has a very large prolate quadrupole deformation β2 ≈ 0.4. Within the mean-field theory, this has been attributed to the appearance of the large deformed gap at N = Z = 40 in the deformed single-particle spectrum. Consequently, the nucleus Zr can be viewed as a deformed doublymagic system. In addition to shape-coexistence effects, Zr is a great laboratory for isospin physics. Having equal number of protons and neutrons, this nucleus is self-conjugate; hence, it offers a unique venue to study proton-neutron pairing, isospin breaking effects, and the Wigner energy reflecting an additional binding in self-conjugate nuclei and their neighbours. The mass of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus, including the binding energy. Hence, doubly-magic nuclei are significantly lighter, or more bound, compared to their neighbours. Due to a lack of precision mass measurement data on Zr and its neighbours, it is difficult to characterize the size of the shell effect responsible for the large deformation of Zr. To this end, we performed high precision Penning trap mass spectrometry of four neutron-deficient zirconium isotopes – Zr – and analysed the local trends of the binding-energy surface by studying several bindingenergy indicators. To quantify our findings, experimental patterns have been interpreted using global nuclear mass models augmented by a Bayesian model averaging analysis.