Vacuum polarization in light two-electron atoms and ions

A general theory of the vacuum polarization in light atomic and muon-atomic systems is considered. We derive the closed analytical expression for the Uehling potential and evaluate corrections on vacuum polarization for the 11S-state of the two-electron 3He and 4He atoms and for some two-electron ions, including the Li+, Be2+, B3+ and C4+ ions. The correction for vacuum polarization in two-electron He atoms has been evaluated as ΔEueh ≈ 7.253 ± 0.0025 × 10−7 a.u. The analogous corrections in the two-electron He-like ions rapidly increase with the nuclear charge Q (ΔEueh ≈ 2.7061 × 10−6 a.u. for the Li+ ion and ΔEueh ≈ 2.3495 × 10−5 a.u. for the C4+ ion). The corresponding corrections have also been evaluated for the electron-nucleus and electron-electron interactions.