Redefined vacuum approach and gauge-invariant subsets in two-photon-exchange diagrams for a closed-shell system with a valence electron

Abstract

The two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In contrast to other methods, the redefined vacuum approach enables the identification of eight gauge-invariant subsets and, thus, efficiently checks the consistency of the obtained results. The gauge invariance of found subsets is demonstrated both analytically (for an arbitrary state) as well as numerically for 2s, 2p1/2, and 2p3/2 valence electrons in Li-like ions. Identifying gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, e.g., three-photon exchange, where the fragmentation on simpler subsets is crucial for its successful calculation.

References in corpus (20)

• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms
• QED calculation of the n=1 and n=2 energy levels in He-like ions
• QED tests with highly-charged ions
• Relativistic recoil, electron-correlation, and QED effects on the 2p_j-2s transition energies in Li-like ions
• Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• QED calculation of the 2p3/2-2p1/2 transition energy in five-electron ion of argon
• QED treatment of electron correlation in Li-like ions
• Many-electron QED corrections to the g factor of lithiumlike ions
• QED calculation of the ground-state energy of berylliumlike ions
• Evaluation of the screened QED corrections to the g factor and the hyperfine splitting of lithiumlike ions
• $g$ Factor of Lithiumlike Silicon: New Challenge to Bound-State QED
• Ground-state ionization energies of boronlike ions
• Ionization energies along beryllium isoelectronic sequence
• QED calculations of the $n=2$ to $n=1$ x-ray transition energies in middle-$Z$ heliumlike ions
• Evaluation of the low-lying energy levels of two- and three-electron configurations for multi-charged ions
• Evaluation of the two-photon exchange diagrams for the $(1s{)}^{2}2p_{3/2}$ electron configuration in Li-like ions
• QED radiative corrections to the ${}^2$P${}_{1/2}$-${}^2$P${}_{3/2}$ fine-structure in fluorinelike ions
• Many-electron effects in the hyperfine splitting of lithiumlike ions

Cited by in corpus (4)

• Two-photon exchange corrections to the $g$ factor of Li-like ions
• All-order Coulomb corrections to Delbrück scattering above the pair production threshold
• QED approach to valence-hole excitation in closed shell systems
• Insight into the prospective evaluation of third-order interelectronic corrections on Li-like ions