ABSTRACT
One-Electron HCIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 14.5 Second-Order Radiative Corrections to the Energy Levels in
One-Electron HCIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 14.6 Other One-Electron Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 394 14.7 Many-Electron Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 14.8 Line Profile Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 14.9 Evaluation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 14.10 Evaluation of Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . 410 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
During the past 30 years or so, the quantum electrodynamics (QED) theory of atoms and ions became a routine procedure for the description of the properties of electronic shells in atomic systems. This can be explained by the outstanding progress in the experimental investigations of two kinds of the “new” atomic systems: highly charged ions (HCIs) and superheavy atoms. While for the description of the superheavy atoms, that is, the systems containing more than 100 electrons, the sophisticated methods of the relativistic many-body theory (such as the superposition of configurations or the coupled clusters) are of the primary importance, the theory of ions with few electrons and the nuclear charge Z ≥ 50 can be developed on the basis of QED perturbation theory. The formulation of the QED perturbation theory for the tightly bound electrons is not trivial, and unlike the QED theory of the loosely bound electrons in the light atoms cannot be essentially similar to the free electron QED. During the last decades, a number of general methods based on the S-matrix or the Green function
Ion
were applied for the QED description of the tightly bound electrons in HCIs: adiabatic S-matrix approach [1], two-time Green’s function method (TTGFM) [2], covariant evolution operator (CEO) approach [3], and the line profile approach (LPA) [4]. In this chapter, we will describe the recent status of the QED theory of HCIs. As a theoretical tool, we will use exclusively S-matrix methods [1,4], but the practical results obtained by all the methods will be discussed and compared.
