Electron shielding of the nuclear magnetic moment in a hydrogenlike atom

We obtain the shielding of the nuclear magnetic moment by an electron in the $n{s}_{1∕2}$ state in a hydrogenlike ion with arbitrary nuclear charge $Z$. The calculation is based on the decomposition of the shielding correction into two terms corresponding to the intermediate states with $j=1∕2$ and $3∕2$. The former is evaluated using the $j=1∕2$ projection of the correction to the electron wave function due to the external magnetic field, while the latter is calculated by applying the $j=3∕2$ projection of the correction to the wave function due to the hyperfine interaction between the electron and the nucleus.