Precision Test of Many-Body QED in theBe+2pFine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the $2s\text{ }{^{2}S}_{1/2}\ensuremath{\rightarrow}2p\text{ }{^{2}P}_{1/2,3/2}$ transitions in ${\mathrm{Be}}^{+}$ were measured for the isotopes $^{7,9--12}\mathrm{Be}$. The fine structure splitting of the $2p$ state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of $m{\ensuremath{\alpha}}^{6}$ and $m{\ensuremath{\alpha}}^{7} \mathrm{ln} \ensuremath{\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.