$(Z\alpha)^{4}$ order of the polarization operator in Coulomb field at   low energy
  We derive the low-energy expansion of $(Z\alpha) ^{2}$ and $(Z\alpha) ^{4}$ terms of the polarization operator in the Coulomb field. Physical applications such as the low-energy Delbr\"{u}ck scattering and "magnetic loop" contribution to the $g$ factor of the bound electron are considered. 
G. G. Kirilin, R. N. Lee