Precision spectroscopy on $^9$Be overcomes limitations from nuclear structure

TL;DR

This study achieves high-precision spectroscopy of $^9$Be ions, providing critical benchmarks for nuclear magnetic properties and testing quantum electrodynamics, thereby overcoming previous limitations caused by nuclear structure uncertainties.

Contribution

First high-precision measurements of hyperfine and Zeeman structures in hydrogen-like $^9$Be$^{3+}$, enabling testing of nuclear models and QED calculations with unprecedented accuracy.

Findings

Determined the effective Zemach radius with 500 ppm uncertainty.

Measured the nuclear magnetic moment with 0.6 ppb precision.

Compared charge states to test multi-electron shielding effects.

Abstract

Many powerful tests of the Standard Model of particle physics and searches for new physics with precision atomic spectroscopy are plagued by our lack of knowledge of nuclear properties. Ideally, such properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. While 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. Here, we focus on $^9$Be which offers the unique possibility to utilize 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 the first high-precision spectroscopy of the $1s$ hyperfine and Zeeman structure in hydrogen-like $^9$Be$^{3+}$. We determine its effective Zemach radius with an uncertainty of $500$ ppm, and its bare nuclear magnetic moment with an uncertainty of $0.6$ parts-per-billion (ppb) - uncertainties unmatched beyond hydrogen. Moreover, we compare to measurements conducted on the three-electron charge state $^9$Be$^{+}$, which, for the first time, enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the ppb level. In addition, we test quantum electrodynamics (QED) methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark essential for transferring high-precision results of nuclear magnetic properties across different electronic configurations.