Research Background
The size of a nucleus (nuclear charge radius) is an important physical quantity that reflects the arrangement of protons and neutrons within the nucleus. Particularly in deformed nuclei, such as those of rare earth elements, examining changes in the charge radius can deepen our understanding of nuclear structure and nuclear deformation.
Until now, electron scattering experiments, muon atomic spectroscopy, and laser spectroscopy of neutral atoms and singly charged ions have been used to measure nuclear radii; however, it has not been easy to directly compare different elements.
For lutetium (Lu) and ytterbium (Yb), evaluations based on past experiments had presented an anomalous trend not observed in other rare-earth elements: the nucleus of lutetium, which has an odd number of protons, is larger than that of the adjacent even-proton nucleus. This had remained an unsolved problem for many years.
Research Findings
To evaluate nuclear radii, the international collaborative research group focused on the effect in which the size of the nucleus causes a shift in the atom's energy levels (volume shift*1). Normally, this energy shift is extremely small. This is because the size of the nucleus is so tiny relative to the bound electrons in the atom that the relationship is virtually imperceptible. Therefore, the international collaborative research group adopted highly charged ions (HCIs)*2 as the spectroscopic target to amplify this shift and accurately evaluate the nuclear radius. Since the bound electrons in HCIs are located in the vicinity of the nucleus, the volume shift is strongly reflected in the energy levels (Figure 1).
In the experiment, we generated HCIs of lutetium (Lu) and ytterbium (Yb) using Tokyo-EBIT (Fig. 2) *3 at the University of Electro-Communications. We alternately measured high-resolution extreme ultraviolet emission spectra and compared the emission line energies of Lu59+, Lu60+, Yb58+, and Yb59+ (Fig. 3). Using the latest high-precision atomic structure calculations, we converted the observed differences in emission line energies into differences in nuclear radii, which revealed that the nucleus of lutetium (atomic number 71) is slightly smaller than that of ytterbium (atomic number 70) (Fig. 4). This result suggests that the expected odd-even staggering in the atomic-number dependence of nuclear radii*4 in the rare-earth region holds for Yb-Lu, implying that the long-debated "reversal problem" regarding the lutetium nuclear radius has been resolved.
Significance of the Research Findings and Future Directions
In this study, we demonstrated that the nuclear radii of heavy elements can be evaluated using extreme ultraviolet spectroscopy of HCIs. In particular, this method enables "direct comparisons between different elements"—which was difficult to achieve using conventional techniques such as laser spectroscopy of neutral atoms or singly charged ions—and provides a new approach to nuclear structure research in the heavy-element region.
Furthermore, the nuclear radii of rare-earth elements obtained in this study not only call into question the picture based on conventional experimental data but also suggest the existence of significant even-odd effects that cannot be fully explained by current nuclear structure theories, thereby highlighting new challenges in the study of heavy deformed nuclei.
Going forward, we will expand our research scope beyond the elements studied in this work—lutetium and ytterbium—to include neighboring rare-earth elements and radioactive nuclides, in order to determine whether this phenomenon is general or specific to certain nuclides. Systematic measurements using HCI spectroscopy are expected to lead to new insights into nuclear structure.
Furthermore, this research applies HCI spectroscopy—a technique cultivated to date for advancing our understanding of relativistic atomic physics and the development of nuclear fusion science—to nuclear research. Through this study, we were able to further refine related HCI spectroscopy techniques, such as high-precision wavelength analysis, rare-earth element injection methods into the experimental apparatus, and high-precision atomic structure calculations. Going forward, we will vigorously pursue HCI spectroscopy research using these techniques, aiming to contribute to a wide range of interdisciplinary research fields, including fusion plasma diagnostics, astrophysics, and the development of short-wavelength light sources.
[Glossary]
*1 Volume Shift
A phenomenon in which the atomic energy levels change slightly due to differences in the "size" (volume or charge distribution) of the nuclide.
*2 Highly Charged Ions (HCIs)
A general term for atoms or molecules with a positive or negative charge of two or more. Here, it refers to atomic ions (cations) from which a large number of electrons have been stripped.
*3 Tokyo-EBIT
EBIT stands for "Electron Beam Ion Trap" providing a laboratory plasma in which a monoenergetic electron beam is compressed by a magnetic field to achieve high density. When atoms are introduced into the EBIT, frequent collisions with electrons occur, leading to successive ionization processes that generate highly charged ions. Tokyo-EBIT is an EBIT device developed at the University of Electro-Communications in the 1990s and has been in operation for a long time. It boasts world-class performance in both electron beam energy and current, enabling the generation and observation of the emission from ions of various elements in a wide range of charge states.
*4 Odd-Even Staggering Observed in Nuclear Radii
The size of a nucleus does not merely vary smoothly as the number of protons or neutrons changes; rather, it exhibits a slight zigzag pattern between nuclei with an even number of protons (atomic number) and those with an odd number. This regular variation is called "odd-even staggering." Odd-even staggering reflects the forces acting within the nucleus and the tendency of protons and neutrons to form pairs, providing a crucial clue for understanding nuclear structure. This study suggests that this odd-even staggering may be more pronounced than previously thought, raising new challenges that current theories cannot fully explain.
