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Repair Windows errors before they cause bigger problemsFix Now →Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Clear out junk files and repair common Windows errorsFree Scan →An international team has demonstrated a spectroscopy method that compares nuclear charge radii across different heavy elements. Using highly charged lutetium and ytterbium ions in the Tokyo-EBIT apparatus, the researchers measured extreme-ultraviolet emission lines and found that the natural-abundance-averaged lutetium nucleus is slightly smaller than ytterbium’s.
Published in Nature Communications on 26 September 2026, the result overturns the long-standing Lu–Yb radius ordering inferred from older recommended values, restores the expected odd-even pattern for nuclei with neutron number 94, and exposes a gap in current nuclear-structure theory.
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How spectroscopy can measure a nuclear radius
Atoms do not have a hard-edged nuclear boundary that can be viewed directly. Instead, spectroscopy detects how the finite size of the nucleus changes an electron’s energy.
A nucleus with a larger charge radius produces a slightly different electric field inside the region occupied by the electrons. That changes atomic energy levels through the nuclear-volume, or field, shift. The effect is normally extremely small because the nucleus is tiny compared with the electron cloud.
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The new experiment increases the signal by stripping away most of each atom’s electrons. In a highly charged ion, the remaining bound electrons are held much closer to the nucleus and are therefore more sensitive to its charge distribution. The team measured high-resolution extreme-ultraviolet (EUV) emission-line energies from four charge states:
- Lu59+
- Lu60+
- Yb58+
- Yb59+
Relativistic atomic-structure calculations then related the measured line-energy differences to the difference in nuclear charge radius. The calculation step is essential: the observed spectral shifts are not themselves a radius measurement until atomic theory converts them into nuclear-structure information.
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What Tokyo-EBIT contributes
Tokyo-EBIT is the experiment’s electron-beam ion-trap source. It creates and confines ions in very high charge states, making the Lu and Yb transitions accessible for EUV spectroscopy. Producing those ions, injecting rare-earth material into the apparatus, and resolving their wavelengths are all specialized parts of the measurement.
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The collaboration involved researchers centered at the National Institute for Fusion Science, the University of Electro-Communications, Clemson University and the University of Grenoble-Alpes. Their approach combines ion-trap technology, EUV wavelength measurement and high-precision relativistic calculations rather than relying on a single instrument or a direct image of a nucleus.
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What the Lu–Yb comparison found
The measured comparison used natural-abundance-averaged lutetium and ytterbium, so it describes the abundance-weighted samples rather than reporting a radius for one isolated isotope. The direction of the result is clear: lutetium (atomic number 71) has a slightly smaller nuclear charge radius than ytterbium (atomic number 70). The available report does not give a standalone numerical radius difference.
Why the ordering was surprising
Lutetium and ytterbium sit next to each other in the neutron-number-94 isotonic chain: both have 94 neutrons, while their proton numbers differ by one. Nuclear charge radii usually show an odd-even staggering along such chains. Earlier recommended Lu–Yb values instead suggested an inversion in which lutetium appeared larger, creating a long-standing anomaly.
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The new ordering removes that inversion and restores the expected N=94 odd-even staggering. “Resolves” here means that the experimental comparison establishes the ordering responsible for the anomaly; it does not mean that every detail of the underlying nuclear interaction is now explained.
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Nuclear charge radii have traditionally been studied with electron scattering, muon-atom spectroscopy, and laser spectroscopy of neutral atoms or singly charged ions. Those techniques remain important, but comparing different elements directly is difficult because each method has its own reference systems, atomic corrections and experimental constraints.
| Approach | Direct comparison between different elements | What determines sensitivity | Heavy or radioactive systems | Infrastructure |
|---|---|---|---|---|
| Electron scattering | Historically not straightforward for precision Lu–Yb comparisons | Scattering response to the nuclear charge distribution | Depends on an appropriate target and beam; no general radioactive extension is established here | High-energy beam and scattering facility |
| Muon atomic spectroscopy | Historically not straightforward for direct inter-element comparisons | Muon wavefunction’s strong overlap with the nucleus | Requires production and capture of suitable muonic atoms | Muon source and precision x-ray spectroscopy |
| Neutral or singly charged laser spectroscopy | Excellent for isotope shifts, but cross-element comparisons are difficult | Small isotope- and field-shift changes in optical transitions | Established for selected systems; broader access varies by element | Laser spectroscopy and detailed atomic modeling |
| Highly charged-ion EUV spectroscopy | Designed to enable direct comparisons between different elements | Bound electrons approach the nucleus, amplifying the volume shift | Extension to neighboring rare-earth and radioactive nuclides is planned | EBIT ion source, EUV wavelength measurement and relativistic atomic calculations |
Why the result matters for nuclear theory
The measurement is not only a new way to obtain a radius. It also supplies a stringent test for models of the nucleus. Nuclear-density-functional calculations that include quantified uncertainties reproduce charge-radius staggering along isotopic chains and in semi-magic nuclei, but the reported Lu–Yb comparison shows that they fail to reproduce the large staggering observed along this N=94 isotonic chain.
That mismatch indicates that an important ingredient of the proton-number dependence, pairing behavior or deformation-related structure is not being captured strongly enough by current calculations. The experiment therefore turns a previously disputed ordering into a quantitative benchmark for future models, even though the published summary does not provide a numerical radius difference for model-to-data residuals.
What researchers plan to measure next
The collaboration intends to apply the method to neighboring rare-earth elements and to radioactive nuclides. Those measurements can test whether the large isotonic effect is a broad feature of the region or is unusually strong for particular nuclei.
Further work also builds on technical improvements made for this experiment, including refined wavelength analysis, more reliable rare-earth injection into the ion-trap apparatus and higher-precision atomic-structure calculations. A systematic set of highly charged-ion measurements could connect charge-radius trends across isotopes and isotones using one internally consistent spectroscopic strategy.
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