QED calculation of the nuclear magnetic shielding for hydrogenlike ions

We report an ab initio calculation of the shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions. This investigation takes into account several effects that have not been calculated before to our knowledge (electron self-energy, vacuum polarization, nuclear-magnetization distribution), thus bringing the theory to the point where further progress is impeded by the uncertainty due to nuclear-structure effects. The QED corrections are calculated to all orders in the nuclear binding strength parameter and, independently, to the leading order in the expansion in this parameter. The results obtained lay the groundwork for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions