Ground State Hyperfine Splitting of Hydrogenlike207Pb81+by Laser Excitation of a Bunched Ion Beam in the GSI Experimental Storage Ring

Using a new bunched-beam technique in the GSI heavy-ion experimental storage ring (ESR), we performed precision laser spectroscopy on relativistic heavy ions in the hitherto inaccessible infrared optical region. We determined the wavelength of the $M1\mathrm{}$ transition between the $F=1\mathrm{}$ $\left(\tau \approx 50\mathrm{ms}\right)$ and $F=0\mathrm{}$ hyperfine states of the $1s$ ground state of hydrogenlike ${}^{207}{\mathrm{Pb}}^{81+}$. Comparing the result of 1019.7(2) nm with very recent theoretical predictions concerning QED and nuclear size contributions, a disagreement of 4.5 nm is found. Since the nucleus of ${}^{207}{\mathrm{Pb}}^{81+}$ is well described by the single-particle shell model, uncertainties in nuclear corrections are expected to be small.