Precision spectroscopy on ⁹Be overcomes limitations from nuclear structure

Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei^1-4. Here we focus on ⁹Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like ⁹Be³⁺. We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion- uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state ⁹Be⁺ (ref. ⁵), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations.