Atomic nuclei exhibit single-particle and collective degrees of freedom, making them susceptible to variations in size and shape when adding or removing nucleons. The rare cases where dramatic changes in shape occur with the removal of only a single nucleon are key for pinpointing the components of the nuclear interaction driving nuclear deformation. Laser spectroscopy probes the nuclear charge distribution, revealing attometer-scale variations and highlighting sensitivity to the proton (Z) and neutron (N) configurations of the nucleus. The lead isotopes, which possess a closed proton shell (Z = 82), are spherical and steadily shrink with decreasing N. A surprisingly different story was observed for their close neighbours, the mercury isotopes (Z = 80) almost half a century ago 1, 2 : Whilst the even-mass isotopes follow the trend seen for lead, the odd-mass isotopes 181,183,185 Hg exhibit a striking increase in charge radius. This dramatic 'shape staggering' between evenand odd-mass isotopes remains a unique feature of the nuclear chart. Here we present the extension of laser spectroscopy results that reach 177 Hg. An unprecedented combination of state-of-theart techniques including resonance laser ionization, nuclear spectroscopy and mass spectrometry, has established 181 Hg as the shape-staggering endpoint. Accompanying this experimental tour de force, recent computational advances incorporating the largest valence space ever used have been exploited to provide Monte-Carlo Shell Model calculations, in remarkable agreement with the experimental observations. Thus, microscopic insight into the subtle interplay of nuclear interactions that give rise to this phenomenon has been obtained, identifying the shape-driving orbitals. Although shape staggering in the mercury isotopes is a unique and localized feature in the nuclear chart, the underlying mechanism that has now been uncovered nicely describes the duality of single-particle and collective degrees of freedom in atomic nuclei.

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Neutron-deficient 177−185 Hg isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility, in an experiment combining different detection methods tailored to the studied isotopes. These include either α-decay tagging or Multireflection Time-of-Flight gating to identify the isotopes of interest. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of 177−180 Hg. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole and electric quadrupole moments of the odd-A isotopes and arguments in favor of I = 7/2 spin assignment for 177,179 Hg were deduced. Experimental results are compared with Density Functional Theory (DFT) and Monte-Carlo Shell Model (MCSM) calculations. DFT calculations with several Skyrme parameterizations predict a large jump in the charge radius around the neutron N = 104 mid shell, with an odd-even staggering pattern related to the coexistence of nearly-degenerate oblate and prolate minima. This near-degeneracy is highly sensitive to many aspects of the effective interaction, a fact that renders perfect agreement with experiment out of reach for current functionals. Despite this inherent difficulty, the SLy5s1 and a modified UNEDF1 SO parameterization predict a qualitatively correct staggering that is off by two neutron numbers. MCSM calculations of states with the experimental spins and parities show good agreement for both electromagnetic moments and the observed charge radii. A clear mechanism for the origin of shape staggering within this context is identified: a substantial change in occupancy of the proton πh 9/2 and neutron νi 13/2 orbitals.

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