Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

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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Characterization of the shape-staggering effect in mercury nuclei

Resonance ionization spectroscopy of nobelium (atomic number 102) reveals its ground-state transition and an upper limit for its ionization potential, paving the way to characterizing even heavier elements via optical spectroscopy. Characterizing the heaviest elements in the periodic table is a gruelling task because they are radioactive, exist only for split seconds at a time and need to be artificially produced in sufficient quantities by complicated procedures. The heaviest element that has been characterized by optical spectroscopy is fermium, which has an atomic number of 100. Mustapha Laatiaoui et al. extend the methods used for fermium to perform optical spectroscopy on nobelium (atomic number 102). Through laser resonance ionization spectroscopy, they identify the ground-state transition of the atom and manage to investigate highly excited states called Rydberg states. This allows them to determine an upper limit for the atomic ionization potential of nobelium. This study opens the door to the characterization of even heavier elements such as lawrencium using optical spectroscopy. Optical spectroscopy of a primordial isotope has traditionally formed the basis for understanding the atomic structure of an element. Such studies have been conducted for most elements1 and theoretical modelling can be performed to high precision2,3, taking into account relativistic effects that scale approximately as the square of the atomic number. However, for the transfermium elements (those with atomic numbers greater than 100), the atomic structure is experimentally unknown. These radioactive elements are produced in nuclear fusion reactions at rates of only a few atoms per second at most and must be studied immediately following their production4, which has so far precluded their optical spectroscopy. Here we report laser resonance ionization spectroscopy of nobelium (No; atomic number 102) in single-atom-at-a-time quantities, in which we identify the ground-state transition 1S0 1P1. By combining this result with data from an observed Rydberg series, we obtain an upper limit for the ionization potential of nobelium. These accurate results from direct laser excitations of outer-shell electrons cannot be achieved using state-of-the-art relativistic many-body calculations5,6,7,8 that include quantum electrodynamic effects, owing to large uncertainties in the modelled transition energies of the complex systems under consideration. Our work opens the door to high-precision measurements of various atomic and nuclear properties of elements heavier than nobelium, and motivates future theoretical work.

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Atom-at-a-time laser resonance ionization spectroscopy of nobelium

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.

Proton superfluidity and charge radii in proton-rich calcium isotopes

Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N=126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency.

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M.R. Pearson

Papers

Laser spectroscopy for nuclear structure physics