Researchers used high-precision nuclear calculations to compute a quantity called the Zemach radius for light nuclei up to nine nucleons. The Zemach radius describes how the nucleus’s electric charge and magnetization are distributed together. It matters because it shifts atomic energy levels that are now measured so precisely that tiny nuclear-structure corrections must be known accurately.

The team solved the nuclear many-body problem with two quantum Monte Carlo methods: variational Monte Carlo (VMC) and Green’s function Monte Carlo (GFMC). They started from modern nuclear forces derived in chiral effective field theory and used a family of so‑called Norfolk two‑ and three‑body interaction models. Electromagnetic currents that act between pairs of nucleons were included, because these “two‑body currents” are known to affect electromagnetic observables. The authors evaluated charge and magnetic form factors and integrated them to obtain Zemach radii and the related third electric Zemach moment.

This work is important for interpreting hyperfine splittings and Lamb shifts in both ordinary and muonic atoms. Hyperfine splittings depend directly on the Zemach radius, and the third electric Zemach moment enters the two‑photon exchange correction to the Lamb shift in muonic atoms. Those atomic measurements are used to extract basic nuclear properties. Until now a simple phenomenological Gaussian model has often been used to estimate Zemach effects. Ab initio nuclear calculations like these provide a more microscopic and potentially more reliable input.

The calculations show two notable results. For 6Li, the computed Zemach radius is larger than the value extracted from atomic spectroscopy, in agreement with other recent theoretical work. That outcome suggests the mismatch seen in experiments is not simply an artifact of one particular nuclear model. For 9Be, the computed Zemach radius agrees with the experimental extraction. The paper traces earlier disagreements for 9Be to a model‑dependent choice for the magnetic radius used in phenomenological estimates.