$(Zα)^{4}$ order of the polarization operator in Coulomb field at low energy

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We derive the low-energy expansion of $(Zα) ^{2}$ and $(Zα) ^{4}$ terms of the polarization operator in the Coulomb field. Physical applications such as the low-energy Delbrück scattering and "magnetic loop" contribution to the $g$ factor of the bound electron are considered.
16 pages, 10 figures

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