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International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 205-208
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The QED corrections originate in the quantum nature of both the electromagnetic and electron fields. They can be divided in two categories, radiative and non-radiative. The first one includes self-energy and vacuum polarization, which are the main contributions to the Lamb shift in one-electron atoms. These corrections scale as ![[{Z}^{4}/{n}^{3}]](/teximages/cbch4o2/cbch4o2fi218.svg)
(n being the principal quantum number) and are thus very important for inner shells and high Z. The second category is composed of corrections to the electron–electron interaction that cannot be accounted for by RMBPT or MCDF. These corrections start at the two-photon interaction and include three-body effects. The two-photon, non-radiative QED contribution has been calculated recently only for the ground state of two-electron ions (Blundell, Mohr, Johnson & Sapirstein, 1993![[link]](/graphics/greenarr.gif)
; Lindgren, Persson, Salomonson & Labzowsky, 1995) and cannot be evaluated in practice for atoms with more than two or three electrons.
The radiative corrections split up into two contributions. The first contribution is composed of one-electron radiative corrections (self-energy and vacuum polarization). For the self-energy and ![[{Z}\gt10]](/teximages/cbch4o2/cbch4o2fi219.svg)
, one must use all-order calculations (Mohr, 1974a,b, 1975, 1982, 1992; Mohr & Soff, 1993). Vacuum polarization can be evaluated at the Uehling (1935) and Wichmann & Kroll (1956) level. Higher-order effects are much smaller than for the self-energy (Soff & Mohr, 1988) and have been neglected. The second contribution is composed of radiative corrections to the electron–electron interaction, and scales as ![[{Z}^{3}/{n}^{3}]](/teximages/cbch4o2/cbch4o2fi220.svg)
. Ab initio calculations have been performed only for few-electron ions (Indelicato & Mohr, 1990, 1991). Here we use the Welton approximation which has been shown to reproduce very closely ab initio results in all examples that have been calculated (Indelicato, Gorceix & Desclaux 1987; Indelicato & Desclaux 1990; Kim, Baik, Indelicato & Desclaux, 1991; Blundell, 1993a,b).
References
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