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

Abstract

The two-time Green 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. PACS number(s): 12.20.Ds, 31.30. Jv

Calculation of differential cross section for dielectronic recombination with two-electron uranium

“…The importance of the Breit interaction is explained by large sensitivity of the widths of three-electron energy levels to the Breit interaction. Within the framework of the standard QED theory, the energy shift of energy levels (due to the interaction with quantized electromagnetic and electron-positron fields) is commonly written as ∆E = Re{∆E} − i Γ 2 [20,22,27,30], where Re{∆E} is a correction to the energy, Γ defines the width of the energy level. For the one-and two-electron configurations the major contribution to the width of energy level is given by the electron self-energy Feynman graph.…”

“…To study the cross section of the dielectronic recombination with highly charged ions, the QED calculations of the radiative transitions amplitudes between three-electron configurations are necessary. Such calculations can be performed with employment of various methods [12,[19][20][21][22][23]. In the present paper the line-profile approach was used [22].…”

Parity nonconservation effect in the resonance elastic electron scattering on heavy He-like ions

“…is constructed by subtraction of the terms corresponding to the direct part of the interelectronic interaction from τ (1) [26,27] for details). Here I is the operator of the interelectronic interaction, |Ψ i and |Ψ f are the wave functions of the initial and final states of the system, respectively.…”

“…The second-order amplitude, corresponding to the dielectronic recombination into one of doubly excited d 1 or d 2 states with subsequent Auger decay, is given by [26,27] …”

QED Effects in Heavy Few-Electron Ions

“…This leads to quantum electrodynamics in the Furry picture. To formulate the perturbation theory for calculations of the energy levels, transition and scattering amplitudes, it is convenient to use the two-time Green function method [4]. For very heavy ions the parameter 1/Z becomes comparable with α and, therefore, all the corrections may be classified by the parameter α only.…”