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 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.
Highlights
Few-electron highly-charged ions are widely considered as important tools in testing quantum electrodynamics (QED) theory in the presence of the binding nuclear field [1,2,3]
With the present work we summarize the computational technique developed for calculations of various QED corrections with the bound-electron propagators, paying particular attention to the notoriously problematic diagrams with several propagators inside the radiative photon loop
In this paper we described the technique used in modern calculations of QED corrections with the bound-electron propagators, including the notoriously problematic diagrams with several propagators inside the radiative photon loop
Summary
Few-electron highly-charged ions are widely considered as important tools in testing quantum electrodynamics (QED) theory in the presence of the binding nuclear field [1,2,3]. Since the nuclear field in highly-charged ions is strong, its binding strength cannot be used as an expansion parameter and theoretical investigations of QED effects should be carried out to all orders in Zα, where Z is the nuclear charge number and α is the fine structure constant This is achieved by working in the so-called Furry picture, where the classical binding field of the nucleus is included into the zeroth-order approximation. The number and the complexity of QED calculations performed to all orders in the binding field has been increasing rapidly These calculations have been successful in improving the achievable precision and in extending the range of the studied effects, from the classical Lamb shift to the QED corrections to the hyperfine structure, the g factor, the transition amplitudes, the nuclear magnetic shielding, etc.
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