Transition energy and lifetime for the ground-state hyperfine splitting of high-Zlithiumlike ions

The ground-state hyperfine splitting values and the transition probabilities between the hyperfine structure components of high-$Z$ lithiumlike ions are calculated in the range $Z=49\mathrm{}$–83. The relativistic, nuclear, QED, and interelectronic interaction corrections are taken into account. It is found that the Bohr-Weisskopf effect can be eliminated in a combination of the hyperfine splitting values of the hydrogenlike and lithiumlike ions of an isotope. This gives a possibility for testing the QED effects in a combination of the strong electric and magnetic fields of the heavy nucleus. Using the experimental result for the $1s$ hyperfine splitting in ${}^{209}{\mathrm{Bi}}^{82+}$, the $2s$ hyperfine splitting in ${}^{209}{\mathrm{Bi}}^{80+}$ is calculated to be $\Delta E=0.7976\mathrm{}\left(2\right)\mathrm{}$ eV.