Virtual light-by-light scattering and thegfactor of a bound electron

Abstract

The contribution of the light-by-light diagram to the $g$ factor of an electron and muon bound in a Coulomb field is obtained. For an electron in a ground state, our results are in good agreement with the results of other authors obtained numerically for large $Z$. For relatively small $Z$ our results have essentially higher accuracy as compared to the previous ones. For muonic atoms, the contribution is obtained with a high accuracy in the whole region of $Z$.