Atomic Spectroscopy of Highly Charged Ions Resolves a Decades-Old Nuclear Radius Puzzle

For decades, one of the quiet oddities of nuclear physics has lurked in the rare-earth region of the periodic table. Measurements of nuclear charge radii, the effective size of the positively charged heart of an atom, seemed to suggest that lutetium, an odd-proton nucleus with atomic number 71, was somehow larger than ytterbium, its even-proton neighbor with atomic number 70. That pattern ran directly counter to the odd-even staggering seen everywhere else among the deformed rare-earth nuclei, and no amount of reanalysis of the older data could make the anomaly disappear. Now an international collaboration led by the National Institute for Fusion Science, together with the University of Electro-Communications, Clemson University, and Grenoble Alpes University, has shown that the anomaly was an artifact of how the radii were being compared, not a genuine quirk of the nuclei themselves.

The team’s solution was to abandon the traditional measurement strategies altogether and instead interrogate the nucleus through its own electrons, stripped down to a bare handful. In a study published in Nature Communications, the researchers performed high-precision extreme ultraviolet spectroscopy of highly charged ions, atoms from which dozens of electrons have been removed, using the Tokyo-EBIT facility at the University of Electro-Communications. By measuring the emission line energies of lutetium ions carrying charges of 59+ and 60+ and ytterbium ions carrying charges of 58+ and 59+, and comparing those energies against state-of-the-art atomic structure calculations, they extracted the tiny influence of nuclear size on atomic energy levels. The verdict: the lutetium nucleus is actually slightly smaller than that of ytterbium, exactly as the expected odd-even staggering predicts.

To understand why this measurement required such an exotic approach, it helps to consider what a nuclear charge radius actually is and how it normally gets measured. The nucleus is astonishingly small compared with the cloud of electrons that surrounds it, typically by a factor of tens of thousands. When an electron orbits far from the nucleus, as it does in a neutral atom or a singly charged ion, it spends almost no time inside the nuclear volume, so the finite size of the nucleus barely perturbs its energy. The resulting energy shift, known as the volume shift, is real but minuscule, and teasing it out of optical spectra has historically required exquisite laser spectroscopy and careful comparisons, usually within a single element across a chain of isotopes. Comparing radii between different elements was notoriously difficult, because the atomic physics differences between neighboring elements swamp the nuclear signal.

Highly charged ions change the calculus dramatically. When an atom is ionized many times, the remaining electrons are pulled into tight orbits that lie close to the nucleus, in some cases penetrating deep into the nuclear interior. There they directly sample the distribution of nuclear charge, and the volume shift is amplified enormously relative to what a neutral atom would show. A nucleus that is a few percent larger or smaller than its neighbor leaves a measurable fingerprint on the extreme ultraviolet emission lines of these stripped ions. In effect, the highly charged ion acts as an exquisitely sensitive probe that has been threaded directly into the nucleus, converting a nuclear property into an atomic wavelength that can be measured with spectroscopic precision.

The instrument that made this possible is Tokyo-EBIT, an Electron Beam Ion Trap developed at the University of Electro-Communications in the 1990s and refined over decades of operation. Inside the device, a monoenergetic electron beam is compressed by a strong magnetic field to high current density, creating a laboratory plasma unlike any natural one. When atoms of a chosen element are injected into this beam, they collide repeatedly with the fast electrons and are stripped of their electrons in successive steps, climbing the charge-state ladder until they reach the desired ionization stage. Tokyo-EBIT boasts world-class performance in both electron beam energy and current, which allowed the team to generate and observe lutetium and ytterbium ions in the extremely high charge states around 58+ to 60+, where only a handful of bound electrons remain.

The experimental protocol demanded unusual care. The team alternately recorded high-resolution extreme ultraviolet emission spectra of the lutetium and ytterbium ions, switching between elements so that instrumental drifts and plasma conditions would affect both measurements equally. The emission line energies of Lu59+, Lu60+, Yb58+, and Yb59+ were then compared line by line. Because the ions in each pair share nearly identical electronic configurations, the differences in their emission energies could be attributed almost entirely to the nuclear volume shift rather than to ordinary atomic structure effects. The latest high-precision atomic structure calculations served as the theoretical bridge, converting the observed energy differences into differences in nuclear charge radii with a rigor that earlier techniques could not match.

The result settles a puzzle that has lingered through generations of nuclear data compilations. Earlier evaluations, built on electron scattering experiments, muonic atom spectroscopy, and laser spectroscopy of neutral atoms and singly charged ions, had implied that lutetium’s nucleus was larger than ytterbium’s, an apparent reversal of the odd-even staggering that governs nuclear sizes across the rare-earth region. The new measurement shows that no reversal exists. The nucleus of lutetium, with its odd number of protons, is slightly smaller than the even-proton nucleus of ytterbium, in keeping with the zigzag pattern that reflects the pairing tendency of protons and neutrons inside the nucleus. The long-debated reversal problem, as it came to be known, has been resolved.

Yet the resolution of one puzzle opens the door to another. The charge radii of rare-earth elements obtained in this study not only call into question the picture built on conventional experimental data but also suggest that the odd-even effects in this region may be significantly more pronounced than current nuclear structure theories can fully explain. Deformed nuclei, those whose shapes deviate from spherical, dominate the rare-earth region, and their radii encode rich information about collective rotation, pairing correlations, and the interplay of protons and neutrons in a strongly interacting quantum system. If the staggering is stronger than theory predicts, then something important about the nuclear force and the pairing of nucleons in deformed systems remains to be understood, and the rare-earth nuclei are pointing the way.

What makes the demonstration especially significant is its generality. Because the method compares emission line energies of highly charged ions of different elements directly, it enables the kind of cross-element comparison that laser spectroscopy of neutral atoms and singly charged ions could never easily provide. The researchers plan to extend the technique beyond lutetium and ytterbium to neighboring rare-earth elements and to radioactive nuclides, mapping out whether the enhanced odd-even staggering is a general feature of the region or specific to particular nuclei. Systematic measurements across a chain of highly charged ions could deliver a new, self-consistent dataset on nuclear charge radii in the heavy-element region, precisely where deformed nuclei make the physics richest and the traditional methods most strained.

The work also represents a striking repurposing of a technique born in a different corner of physics. Highly charged ion spectroscopy was cultivated over decades to advance relativistic atomic physics and to support nuclear fusion science, where the extreme plasmas of fusion devices strip atoms to high charge states and demand accurate atomic data for diagnostics. The present study shows that the same machinery, together with refined methods of high-precision wavelength analysis, rare-earth element injection into the trap, and high-precision atomic structure calculation, can serve as a precision tool for nuclear structure research. The researchers intend to pursue this line vigorously, with applications extending to fusion plasma diagnostics, astrophysics, and the development of short-wavelength light sources. A puzzle about the size of two adjacent nuclei, probed by electrons that orbit within a whisper of the nuclear surface, has thus become a demonstration that the boundary between atomic and nuclear physics is thinner, and more useful, than anyone had fully appreciated.

Subject of Research: Measurement of nuclear charge radii in rare-earth elements using extreme ultraviolet spectroscopy of highly charged ions

Article Title: Exploring nuclear properties by atomic spectroscopy

Article References: Exploring nuclear properties by atomic spectroscopy. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: nuclear charge radii, highly charged ions, atomic spectroscopy, extreme ultraviolet, Tokyo-EBIT, lutetium, ytterbium, odd-even staggering, rare-earth nuclei, nuclear structure, deformed nuclei, volume shift