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A new highly charged-ion spectroscopy method has directly compared the nuclear charge radii of two different heavy elements. Using extreme-ultraviolet (EUV) emission from lutetium and ytterbium ions, an international collaboration found that lutetium (Z=71) has a slightly smaller natural-abundance-averaged nuclear charge radius than ytterbium (Z=70). The result restores the expected odd-even staggering along the N=94 isotonic chain and overturns the long-standing Lu–Yb inversion implied by older recommended values.
What the experiment measured
The collaboration combined high-resolution EUV spectroscopy with relativistic atomic-structure calculations. At the Tokyo-EBIT facility, researchers produced highly charged ions of lutetium and ytterbium and measured the energies of their emitted EUV lines. The analyzed species were Lu59+, Lu60+, Yb58+ and Yb59+.
Differences between selected line energies are sensitive to the finite size of the nucleus. The team used calculations that include relativistic effects to translate those measured energy differences into a comparison of nuclear charge radii. The published result gives the ordering of the radii, but the available report does not provide a standalone numerical Lu–Yb radius difference, so no specific value should be inferred.
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1Scan for outdated or missing drivers - takes under a minute2Repair Windows errors before they cause bigger problems3Fix the driver behind crashes, sound loss and screen glitchesThe work was reported in Nature Communications on 26 September 2026 by researchers centered at the National Institute for Fusion Science, the University of Electro-Communications, Clemson University and the University of Grenoble-Alpes.
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How spectroscopy reveals nuclear size
The volume shift
Atomic energy levels are affected by the fact that a nucleus has a finite volume rather than being a mathematical point. Electrons that penetrate close to the nucleus experience a slightly different electric potential when the nuclear charge is distributed over a finite radius. That produces a small change in the transition energy, commonly called a nuclear-volume or field shift.
For ordinary neutral atoms and many singly charged ions, the shift is extremely small because the nucleus is tiny compared with the electron cloud. Isolating it also requires separating nuclear-size effects from other isotope and atomic-structure contributions.
Why highly charged ions help
Highly charged ions have had many of their electrons removed. Their remaining bound electrons are held more tightly and spend more of their wavefunction close to the nucleus. That increases the sensitivity of particular transitions to the nuclear charge radius. The experiment therefore uses the ion’s charge state as an amplifier for a signal that is difficult to detect in less highly charged systems.
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The final radius comparison is not obtained by treating a spectral line as a ruler by itself. It depends on calculating the relativistic structure of the selected ions, identifying how the relevant transitions respond to nuclear size, and comparing the calculated sensitivity with the measured EUV line-energy differences.
What Tokyo-EBIT is and why it was needed
Tokyo-EBIT is an electron-beam ion-trap apparatus used to make and confine highly charged ions for precision measurements. An intense electron beam strips electrons from injected atoms and helps trap the resulting positive ions. The trapped ions emit EUV photons as they undergo electronic transitions, allowing their line energies to be measured with high resolution.
This combination of ion production, confinement and EUV detection is central to the method. It provides access to charge states such as those used for Lu and Yb while keeping the ions available long enough for their spectra to be analyzed. The collaboration also refined rare-earth injection into the apparatus and the wavelength analysis needed for the comparison.
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Why lutetium’s radius was thought to exceed ytterbium’s
Lutetium and ytterbium are neighboring elements, with atomic numbers 71 and 70 respectively. Earlier recommended nuclear-radius values placed them in an anomalous order: the Lu value appeared larger than the Yb value for the relevant natural-abundance comparison. That implied an inversion of the odd-even staggering expected along the N=94 isotonic chain.
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Does this resolve the Lu–Yb nuclear-radius anomaly?
For the ordering itself, yes. The direct highly charged-ion comparison removes the Lu inversion anomaly identified from older recommended values: Lu is smaller than Yb in the reported natural-abundance-averaged comparison.
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It does not close every theoretical question. The peer-reviewed abstract states that nuclear-density-functional calculations, even with quantified uncertainties, “fail to reproduce the large stagger.” Those calculations do reproduce charge-radius staggering along isotopic chains and in semi-magic nuclei, but they do not account for the magnitude of the isotonic effect observed here. The experiment therefore both resolves the empirical ordering and exposes a remaining challenge for nuclear-structure theory.
How this method differs from older radius measurements
| Comparison point | Conventional approaches | Highly charged-ion EUV method |
|---|---|---|
| Typical techniques | Electron scattering, muon atomic spectroscopy, or laser spectroscopy of neutral and singly charged atoms | High-resolution EUV spectroscopy of highly charged ions, interpreted with relativistic atomic calculations |
| Direct comparison of different elements | Generally difficult to make on a common spectroscopic basis | Designed to compare neighboring elements directly; the institutional account describes this as enabling “direct comparisons between different elements” |
| Nuclear-size sensitivity | Can be limited by the small field shift in weakly bound electronic systems | Enhanced because remaining electrons in highly charged ions probe closer to the nucleus |
| Reach into heavy or deformed nuclei | Depends strongly on the availability of suitable targets and transitions | Offers a route to systematic studies of heavy and deformed nuclei, subject to suitable ion production and calculations |
| Infrastructure | May use scattering facilities, muon sources or laser-spectroscopy systems | Requires an EBIT-style ion trap, EUV wavelength measurements and high-precision atomic-structure theory |
| Systematic chains | Often optimized for isotope shifts within one element | Can be extended across neighboring rare-earth elements, isotones and selected radioactive nuclides |
Why the result matters beyond Lu and Yb
Most precision nuclear-radius programs compare isotopes of the same element. That strategy is powerful, but it does not make comparisons between different proton numbers straightforward. The new approach supplies a complementary route: choose transitions in highly charged ions whose finite-nuclear-size response can be calculated accurately, then compare line energies across elements.
That capability is especially valuable in heavy and deformed regions of the nuclear chart, where structure changes can be subtle and where conventional methods may not provide a uniform set of measurements. A direct inter-element comparison can test whether a feature belongs to a particular isotope chain, an isotonic chain or a broader region of nuclear structure.
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What happens next
The collaboration plans to apply highly charged-ion spectroscopy to neighboring rare-earth elements and to radioactive nuclides. Those measurements will test whether the large odd-even staggering is a general feature of the region or is unusually strong for the Lu–Yb pair.
Future work will also depend on continuing improvements in three linked areas:
Quick Recap
- Producing and injecting additional rare-earth species into the ion-trap apparatus.
- Refining EUV wavelength and line-energy analysis so very small nuclear-size effects can be separated reliably.
- Extending high-precision relativistic atomic calculations to the charge states and transitions needed for new elements and radioactive nuclides.
What readers should take away
- Highly charged ions amplify the atomic-energy response to nuclear size.
- Tokyo-EBIT EUV spectra enabled a direct comparison between lutetium and ytterbium.
- Lutetium’s reported natural-abundance-averaged nuclear charge radius is slightly smaller than ytterbium’s.
- The result restores the expected N=94 odd-even staggering and overturns the earlier Lu inversion ordering.
- Nuclear-density-functional models currently do not reproduce the large observed isotonic stagger.
- Measurements of other rare-earth and radioactive nuclides are planned to determine how broadly the effect applies.
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