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Nuclear charge radii are sensitive probes of different aspects of the nucleon–nucleon interaction and the bulk properties of nuclear matter, providing a stringent test and challenge for nuclear theory. Experimental evidence suggested a new magic neutron number at N = 32 (refs. 1–3) in the calcium region, whereas the unexpectedly large increases in the charge radii4,5 open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with β-decay detection, we were able to extend charge radii measurements of potassium isotopes beyond N = 32. Here we provide a charge radius measurement of 52K. It does not show a signature of magic behaviour at N = 32 in potassium. The results are interpreted with two state-of-the-art nuclear theories. The coupled cluster theory reproduces the odd–even variations in charge radii but not the notable increase beyond N = 28. This rise is well captured by Fayans nuclear density functional theory, which, however, overestimates the odd–even staggering effect in charge radii. These findings highlight our limited understanding of the nuclear size of neutron-rich systems, and expose problems that are present in some of the best current models of nuclear theory.The charge radii of potassium isotopes up to 52K are measured, and show no sign of magicity at 32 neutrons as previously suggested in calcium. The observations are interpreted with coupled cluster and density functional theory calculations.

Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain ‘magic’ numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly magic features are known in 40,48 Ca, and recently suggested in two radioactive isotopes, 52,54 Ca. Although many properties of experimentally known calcium isotopes have been successfully described by nuclear theory, it is still a challenge to predict the evolution of their charge radii. Here we present the first measurements of the charge radii of 49,51,52 Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly magic nature of 52 Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei. Doubly magic atomic nuclei — having a magic number of both protons and neutrons — are very stable. Now, experiments revealing unexpectedly large charge radii for a series of Ca isotopes put the doubly magic nature of the 52 Ca nucleus into question.

Nuclear charge radii globally scale with atomic mass number A as A 1∕3 , and isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. This odd–even staggering, ubiquitous throughout the nuclear landscape 1 , varies with the number of protons and neutrons, and poses a substantial challenge for nuclear theory 2 – 4 . Here, we report measurements of the charge radii of short-lived copper isotopes up to the very exotic 78 Cu (with proton number Z = 29 and neutron number N = 49), produced at only 20 ions s –1 , using the collinear resonance ionization spectroscopy method at the Isotope Mass Separator On-Line Device facility (ISOLDE) at CERN. We observe an unexpected reduction in the odd–even staggering for isotopes approaching the N = 50 shell gap. To describe the data, we applied models based on nuclear density functional theory 5 , 6 and A -body valence-space in-medium similarity renormalization group theory 7 , 8 . Through these comparisons, we demonstrate a relation between the global behaviour of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects, naturally emerge from A -body calculations fitted to properties of A ≤ 4 nuclei. Isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. In charge radii of short-lived copper isotopes, a reduction of this effect is observed when the neutron number approaches fifty.

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. Although the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus 48 Ca. We show that the neutron skin (difference between the radii of the neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities that are at present targeted by precision measurements. Based on ab initio results for 48 Ca, we provide a constraint on the size of a neutron star. Determining—and defining—the size of an atomic nucleus is far from easy. First-principles calculations now provide accurate information on the neutron distribution of the neutron-rich 48 Ca nucleus—and constraints on the size of a neutron star.

One of the most important global properties of the atomic nucleus is its size. Experimentally determined nuclear charge radii carry unique information on the nuclear force and complex dynamics of protons and neutrons moving inside the nucleus. The intricate behaviour of charge radii along the chain of Ca isotopes, including the unexpectedly large charge radius of neutron-rich 52Ca, poses a daunting challenge for nuclear theory1. Here we present the measurements of the charge radii of proton-rich isotopes 36,37,38Ca, whose properties are impacted by the interplay between nuclear superfluidity and weak binding. Calculations carried out within nuclear density functional theory show that the combination of a novel interaction2 and a state-of-the-art theoretical method can successfully explain the behaviour of charge radii from the lightest to the heaviest Ca isotopes. Through this model, we show how the new data on 36,37,38Ca elucidate the nature of nucleonic pairing in weakly bound proton-rich isotopes.Spectral study on 36,37,38Ca isotopes and calculations based on density functional theory reveal the interplay between charge radii and nucleonic pairing correlations.

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.High-precision mass measurements of exotic zirconium nuclei are reported, and reveal a double-shell closure for the deformed nucleus 80Zr, which is more strongly bound than previously thought.

Superheavy nuclei represent the limit of nuclear mass and charge; they inhabit the remote corner of the nuclear landscape, whose extent is unknown. The discovery of new elements with atomic numbers Z ≥ 110 has brought much excitement to the atomic and nuclear physics communities. The existence of such heavy nuclei hangs on a subtle balance between the attractive nuclear force and the disruptive Coulomb repulsion between protons that favours fission. Here we model the interplay between these forces using self-consistent energy density functional theory; our approach accounts for spontaneous breaking of spherical symmetry through the nuclear Jahn–Teller effect. We predict that the long-lived superheavy elements can exist in a variety of shapes, including spherical, axial and triaxial configurations. In some cases, we anticipate the existence of metastable states and shape isomers that can affect decay properties and hence nuclear half-lives. Superheavy elements, in theory The synthesis of superheavy elements with atomic numbers of 110 and above provides a challenge. These atoms have no real presence in the Universe because of their short lifetimes, but for those brief periods a very large number of particles can hold together to form a nucleus. Theory has to cope with the fact that, despite huge electrostatic repulsion between protons, elements 116 and 118 existed, for a moment. This week's Review Article surveys the latest thinking on superheavy elements with atomic numbers as high as 128.

Understanding the nuclear properties in the vicinity of 100 Sn, which has been suggested to be the heaviest doubly magic nucleus with proton number Z equal to neutron number N , has been a long-standing challenge for experimental and theoretical nuclear physics. In particular, contradictory experimental evidence exists regarding the role of nuclear collectivity in this region of the nuclear chart. Here, we provide further evidence for the doubly magic character of 100 Sn by measuring the ground-state electromagnetic moments and nuclear charge radii of indium ( Z  = 49) isotopes as N approaches 50 from above using precision laser spectroscopy. Our results span almost the complete range between the two major closed neutron shells at N  = 50 and N  = 82 and reveal parabolic trends as a function of the neutron number, with a clear reduction towards these two closed neutron shells. A detailed comparison between our experimental results and numerical results from two complementary nuclear many-body frameworks (density functional theory and ab initio methods) exposes deficiencies in nuclear models and establishes a benchmark for future theoretical developments. Precision laser spectroscopy of ground-state electromagnetic moments and nuclear charge radii of indium shows that 100 Sn has closed proton and neutron shells. The results serve as a benchmark for future theoretical models.

Conservation laws are deeply related to any symmetry present in a physical system 1 , 2 . Analogously to electrons in atoms exhibiting spin symmetries 3 , it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t  = 1/2 (ref.  4 ). Every nuclear state is thus characterized by a total isobaric spin T and a projection T z —two quantities that are largely conserved in nuclear reactions and decays 5 , 6 . A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states 7 , including their ground state, labelled by their total angular momentum J and parity π . Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a J   π  = 5/2 − spin assignment is needed to explain the proton-emission pattern observed from the T  = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its J   π  = 1/2 − mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei. Observations of the decay of 73 Sr, when compared to its mirror nucleus 73 Br, indicate that the spin assignment of their ground states differ, demonstrating mirror-symmetry violation.

A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01192-5.