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

Absolute transition frequencies of the $2s{{}^{2}S}_{1/2}\to 2p{{}^{2}P}_{1/2,3/2}$ 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 $m{\alpha }^6$ and $m{\alpha }^7\hspace{0.17em}\ln \hspace{0.17em}\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.

Figure 1

Fluorescence spectra of ${}^9\mathrm{Be}$ (top row) and ${}^{10}\mathrm{Be}$ (bottom row) in the $2s_{1/2}\to 2p_{1/2}$ (left, $D1$) and the $2s_{1/2}\to 2p_{3/2}$ (right, $D2$) transition as a function of the Doppler-tuning voltage applied to the high-voltage amplifier. A two-component Voigt profile was fitted for each hyperfine component to account for the small satellite peak caused by inelastic collisions. The distance corresponding to the $2p$ fine structure splitting $\mathrm{\Delta }{\nu }_{\mathrm{fs}}$ is indicated.

Figure 2

Experimental results and comparison with theory for the splitting isotope shift (left) and for the fine structure splitting of all isotopes transferred to ${}^9\mathrm{Be}$ (right). The legend belongs to both graphs. The SIS data were clearly improved in run II compared to the previously reported data [22]. Combining all $\mathrm{\Delta }{\nu }_{\mathrm{fs},{}^{\mathrm{A}}\mathrm{Be}\to {}^9\mathrm{Be}}$ results in ${}^9\mathrm{Be}$ fine structure splitting with an accuracy of about 2.5 ppm.