Precision Test of Many-Body QED in the Be$^+$ $2p$ Fine Structure Doublet Using Short-Lived Isotopes

TL;DR

This study precisely measured the transition frequencies in Be$^+$ isotopes to test quantum electrodynamics effects, achieving unprecedented accuracy and confirming theoretical predictions for many-electron systems.

Contribution

It provides the most accurate experimental verification of many-body QED effects in Be$^+$, including relativistic and quantum electrodynamics corrections at high order.

Findings

Excellent agreement between experiment and ab initio calculations.

Achieved two orders of magnitude improvement in accuracy.

Confirmed QED effects in a many-electron system.

Abstract

Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope dependence are extracted and compared to results of \textit{ab initio} calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of $m \alpha^6$ and $m \alpha^7 \ln \alpha$. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.