To interpret the measured values, advanced theory calculations are required too, and those depend on what are known as the fundamental constants. Also, the size of the nuclei in the atoms plays a role. Precise measurements on different atoms and molecules are used to investigate these aspects.
A team of researchers (Kees Steinebach, Jeroen Koelemeij, Hendrick Bethlem, and Kjeld Eikema) at the department of Physics and Astronomy at Vrije Universiteit Amsterdam (VUA) has now performed the most accurate measurement of the internal energy structure of helium atoms. Advanced lasers were used to investigate at which optical frequency (colour) helium absorbs light. A record high accuracy for this atom of nearly 13 digits was achieved, using atomic clocks at VUA and the national metrology institute VSL in Delft though a special fiber connection (‘White Rabbit’). With the incredible precision now achieved, it also becomes possible to improve the determination of the size of the nucleus (the charge radius). This is possible because the finite tiny size of the nucleus still has a (also) tiny influence on the measured energy structure. The advanced theoretical calculations required to interpret the measurements for this have been performed by colleagues at the university of Warsaw (and elsewhere). However, even those calculations are, by themselves, not accurate enough. The team at VUA therefore performed the measurement in two forms of helium, helium-4, the form you find in balloons that has the alpha particle as nucleus, and helium-3, a special form of helium that has a nucleus, the helion, that has one neutron less. The comparison between the two isotopes can be calculated more accurately. The most recent measurement that is published now in Phys. Rev. Lett. has been performed on helium-4 while previously measurements (published in Science in 2025) were performed in helium-3. In both cases the atoms were cooled close to absolute zero temperature and captured in a focused laser beam at the so-called ‘magic wavelength’ In this manner the ultra-cold atoms hardly moved anymore, so that their energy structure could be investigated with record precision.
The measured difference in internal energy structure has resulted now in the most accurate determination of the nuclear charge radius difference between the helium-4 and helium-3 (in technical terms: 1.0676 ± 0.0010 fm2). The result agrees with most other (less accurate) recent determinations. This constitutes an accurate test of a broad range of physics, and it helps interpretation of other and new measurements in the search for new physics. Moreover, as the result is currently much more accurate than nuclear theory calculations, it also sets an important new benchmark for that field.
Paper:
K. Steinebach, J.C.J. Koelemeij, H.L. Bethlem, K.S.E. Eikema, “Spectroscopy of 4He at 0.25 ppt Uncertainty and Improved Alpha-helion Charge-Radius Difference Determination”, Phys. Rev. Lett. 136, 243001 (2026)
This paper in Phys. Rev. Lett. was chosen as Editors’ Suggestion, and a schematic picture of the experiment is featured on the front page of the journal. Also a Synopsis in Physics Magazine about our paper will appear.
Published online 18 June 2026. Below the link to the online version.
https://link.aps.org/doi/10.1103/rwg9-my6x