Vacuum polarization and Wichmann-Kroll correction in the finite basis set approximation

Abstract

The finite basis set method is commonly used to calculate atomic spectra, including QED contributions such as bound-electron self-energy. Still, it remains problematic and underexplored for vacuum-polarization calculations. We fill this gap by trying this approach in its application to the calculation of the vacuum-polarization charge density and the Wichmann-Kroll correction to the electron binding energy in a hydrogen-like ion. We study the convergence of the method with different types and sizes of basis sets. We cross-check our results for the Wichmann-Kroll correction by direct integration of the Green's function. As a relevant example, we consider several heavy hydrogen-like ions and evaluate the vacuum polarization correction for $S$ and $P$ electron orbitals.

10 pages, 7 figures

References in corpus (17)

• High-precision measurement of the atomic mass of the electron
• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• QED calculation of the 2p3/2-2p1/2 transition energy in five-electron ion of argon
• The $g$-factor of light ions for an improved determination of the fine-structure constant
• Progress in quantum electrodynamics theory of highly charged ions
• QED calculation of the ground-state energy of berylliumlike ions
• Vacuum polarization screening corrections to the ground state energy of two-electron ions
• Vacuum polarization calculations for hydrogenlike and alkalilike ions
• Coordinate-space approach to vacuum polarization
• Ab initio calculations of energy levels in Be-like xenon: strong interference between electron-correlation and QED effects
• QED calculation of electron-electron correlation effects in heliumlike ions
• QED radiative corrections to the ${}^2$P${}_{1/2}$-${}^2$P${}_{3/2}$ fine-structure in fluorinelike ions
• Nuclear-size self-energy and vacuum-polarization corrections to the bound-electron g factor
• Calculating the many-potential vacuum polarization density of the Dirac equation in the finite-basis approximation
• Ab initio calculations of the $2p_{3/2}\to 2s$ transition in He-, Li-, and Be-like uranium
• Hadronic vacuum polarization correction to the bound-electron $g$ factor

Cited by in corpus (2)

• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions
• Influence of a Perfectly Conducting Plate on the Uehling Potential of QED