Calculations of QED Effects with the Dirac Green Function

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 need to be performed without any expansion in the nuclear binding strength parameter Z α (where Z is the nuclear charge number and α 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.

6Pe—6Po transitions in boron-like ions with Z = 8–13

The energies, fine structure splittings, transition rates, and lifetimes of inner-shell excited sextet states 1s2s2p2nl, (n = 2–7; l = s, p, d) and 1s2p33p of the boron isoelectronic sequence (Z = 8–13) are investigated using the multi-configuration Rayleigh–Ritz variation method. The mass polarization effect and relativistic corrections are included by first-order perturbation theory. Configuration structures of the high-n inner-shell excited sextet series 6Se,o(m) and 6Pe,o(m) (m = 1–5) of boron-like Na6+ ion are assigned. The wavelengths and transition rates of electric-dipole transitions between 6Pe(m) and 6Po(m) (m = 1–5) states are calculated. The quantum electrodynamics (QED) effects and higher order relativistic corrections are also considered to obtain more accurate transition wavelengths. The predicted transition wavelengths agree well with the available theoretical and experimental data. The lifetimes for the inner-shell excited sextet states 6Pe(m) (m = 1–5) are also reported and discussed with the increase of nuclear charge number, Z. These theoretical data are useful for the identification of spectral lines in experiments and the design of XUV and soft X-ray lasers.

TECHNIQUES IN ANALYTIC LAMB SHIFT CALCULATIONS

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of α(Zα)6 in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.

Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of quantum electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.PACS Nos.: 12.20.Ds, 31.30.Jv, 06.20.Jr, 31.15.–p

On the Dependence of Stark Width and Shift on the Ionization Potential

The simple relations between the Stark broadening parameters and the ionization potential derived by Purić et al. [1] are discussed, and attention is drawn to the serious limitations for their application. The periodic dependence of the Stark width and shift on nuclear charge number obtained by the same authors [2] is also explained.