Insight into the prospective evaluation of third-order interelectronic corrections on Li-like ions

Abstract

Relying on the redefined vacuum state approach, and based on one-particle three-loop Feynman diagrams, partial third-order interelectronic corrections to the valence electron energy shift are investigated in Li-like ions. The idea is to begin with simple one-particle gauge-invariant subsets composed of Feynman diagrams and to keep track of them in the many-electron frame, which is a strong asset of the formalism. An independent derivation is undertaken with the help of perturbation theory to cross-check the expressions. This two-method scheme helps to resolve how the different terms are distributed among three- and four-electron contributions. Furthermore, it provides a tool to overcome the difficulties related to the derivation of reducible terms, which are tricky to deal with. These two independent derivations and the comparison of the resulting expressions are fully consistent, except for two expressions. In these cases, the discrepancy can be traced back to a different topology of the poles.

References in corpus (12)

• Measurement of the Electron Magnetic Moment
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• Direct Bound-Electron $g$ factor Difference Measurement with Coupled Ions
• Many-electron QED corrections to the g factor of lithiumlike ions
• QED calculation of the ground-state energy of berylliumlike ions
• Ab initio calculations of energy levels in Be-like xenon: strong interference between electron-correlation and QED effects
• Self-energy screening effects in the $g$ factor of Li-like ions
• Two-photon exchange corrections to the $g$ factor of Li-like ions
• All-order Coulomb corrections to Delbrück scattering above the pair production threshold
• Redefined vacuum approach and gauge-invariant subsets in two-photon-exchange diagrams for a closed-shell system with a valence electron
• Many-electron effects in the hyperfine splitting of lithiumlike ions
• QED approach to valence-hole excitation in closed shell systems