Observation of the hyperfine transition in lithium-like bismuth ${}^{209}\mathrm{Bi}{}^{80+}$ : Towards a test of QED in strong magnetic fields

We performed a laser spectroscopic determination of the $2s$ hyperfine splitting (HFS) of Li-like ${}^{209}{\text{Bi}}^{80+}$ and repeated the measurement of the $1s$ HFS of H-like ${}^{209}{\text{Bi}}^{82+}$. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum für Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of $\approx 0.71c$. Pulsed laser excitation of the $M1$ hyperfine transition was performed in anticollinear and collinear geometry for ${\text{Bi}}^{82+}$ and ${\text{Bi}}^{80+}$, respectively, and observed by fluorescence detection. We obtain $\Delta E^{\left(1s\right)}=5086.3\left(11\right)\mathrm{meV}$ for ${\text{Bi}}^{82+}$, different from the literature value, and $\Delta E^{\left(2s\right)}=797.50\left(18\right)\mathrm{meV}$ for ${\text{Bi}}^{80+}$. These values provide experimental evidence that a specific difference between the two splitting energies can be used to test QED calculations in the strongest static magnetic fields available in the laboratory independent of nuclear structure effects. The experimental result is in excellent agreement with the theoretical prediction and confirms the sum of the Dirac term and the relativistic interelectronic-interaction correction at a level of 0.5%, confirming the importance of accounting for the Breit interaction.

Figure 1

Experimental setup at the Experimental Storage Ring (ESR). Two ion bunches are formed by applying an rf voltage of twice the ion's revolution frequency to an intraring cavity. The “signal bunch” is repeatedly illuminated with a pulsed, blue-detuned laser for collinear excitation of Li-like ${\text{Bi}}^{80+}$ ions or a red-detuned laser for anticollinear excitation of the H-like ${\text{Bi}}^{82+}\mathrm{ions}$ (not shown). Fluorescence is detected with photomultiplier tubes (PMTs) and individual photon-arrival times relative to the rf phase are processed in a time to digital converter (TDC). A schematic of the new detection system is also shown (see text).

Figure 2

Resonance of the ground-state HFS transition in H-like ${}^{209}{\text{Bi}}^{82+}$ (a) and Li-like ${}^{209}{\text{Bi}}^{80+}$ (b). The signal rate is normalized to the ion current in the ESR and plotted as a function of laser wavelength. The solid line is a error-weighted nonlinear least-square fit of a Gaussian profile without background to the data.