Radiative corrections to the hyperfine-structure splitting of hydrogenlike systems

Abstract

We present a complete calculation of the leading nonrecoil radiative corrections to the $1s$ hyperfine-structure splitting of highly charged hydrogenlike ions. In particular, we have investigated how the radiative corrections for ions with a high nuclear charge number $Z$ are affected by using an extended nuclear magnetization. We also present the first complete evaluation of the Wichmann-Kroll part of the vacuum polarization correction to all orders in $(Z\ensuremath{\alpha})$. To unambiguously incorporate this effect we have also calculated the vacuum polarization correction to the measured nuclear magnetic moment. Total theoretical results are collected for the experimentally interesting ions ${}^{209}{\mathrm{Bi}}^{82+},$ ${}^{207}{\mathrm{Pb}}^{81+},$ ${}^{185}{\mathrm{Re}}^{74+},$ and ${}^{165}{\mathrm{Ho}}^{66+}.$ Also the low-$Z$ region is considered in order to compare with the known part of the $(Z\ensuremath{\alpha})$ expansion.