V. M. Shabaev

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

Abstract The two-time Greens function method in quantum electrodynamics of high- Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.

Dual kinetic balance approach to basis-set expansions for the dirac equation.

A new approach to finite basis sets for the Dirac equation is developed. It does not involve spurious states and improves the convergence properties of basis-set calculations. Efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.

QED calculation of the n= 1 and n=2 energy levels in He-like ions

We perform ab initio QED calculations of energy levels for the

Recoil correction to the bound-electron g factor in H-like atoms to all orders in alphaZ.

n=1

Self-energy correction to the bound-electron g factor in H-like ions.

and

Hyperfine structure of hydrogen-like ions

n=2

GROUND-STATE HYPERFINE SPLITTING OF HIGH-Z HYDROGENLIKE IONS

states of He-like ions with the nuclear charge in the range

Isotope shift in the dielectronic recombination of three-electron ANd57+.

Z=12\text{\char21{}}100

Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high-Z lithiumlike atoms in all orders in alpha Z.

. The complete set of two-electron QED corrections is evaluated to all orders in the parameter

g Factor of Lithiumlike Silicon 28Si11

\ensuremath{\alpha}Z