Calculations of QED effects with the Dirac Green function

Abstract

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects has to be performed without any expansion in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades.

References in corpus (26)

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• QED tests with highly-charged ions
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Cited by in corpus (13)

• QED calculations of energy levels of helium-like ions with $5\le Z\le 30$
• Self-energy screening effects in the $g$ factor of Li-like ions
• Calculating the many-potential vacuum polarization density of the Dirac equation in the finite-basis approximation
• QED calculation of the $2p$ fine structure in Li-like ions
• Two-photon exchange corrections to the $g$ factor of Li-like ions
• High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion
• QED corrections to the correlated relativistic energy: one-photon processes
• One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• Testing inter-electronic interaction in lithium-like tin
• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions
• Two-photon Annihilation of Positrons with K-shell Electrons of H-like ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation