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

TL;DR

This paper derives the low-energy expansion of the polarization operator in Coulomb fields up to order $(Z ext{alpha})^4$, with applications to scattering and bound electron g-factors.

Contribution

It provides the first derivation of the $(Z ext{alpha})^4$ order terms in the polarization operator at low energy, extending previous low-order results.

Findings

Derived explicit formulas for $(Z ext{alpha})^4$ terms

Applied results to Delbrück scattering

Analyzed contributions to the bound electron g-factor

Abstract

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.