QED Theory of Atoms

The QED theory of atoms is reviewed. The principles of QED, the QED theory of the interelectron interaction and the radiative corrections to the energy levels (the Lamb Shift) are considered. The applications of QED to the light atoms and to valence electrons in heavy atoms are discussed. 

The QED theory of the light atoms, apart from the a-expansion exploits also the expansion in parameters aZ where Z is the charge of the nucleus. Thus it is valid only for aZ 1. This condition does not hold for the inner electron shells in heavy atoms. Moreover it does not hold even for the valence electrons in heavy atoms due to the singularity of QED operators. For the evaluation of the matrix elements of such operators the small distances of the electron from the nucleus become important. At such distances the effective electron chOTge Zejf for the valence electrons may not be small. Therefore the QED theory without aZ expansion appears to be necessary. Such theory was first 

Another important application of all-orders in aZ atomic QED is the theory of the multicharged ions. Nowadays all elements of the Periodic Table up to Uranium (Z=92) can be observed in the laboratory as H-like, He-like etc ions. The recent achievements of the QED theory of the highly charged ions (HCI) are summarized in [11], [12]. In principle, the QED theory of atoms includes the evaluation of the QED corrections to the energy levels and corrections to the hyperfine structure intervals, as well as the QED corrections to the transition probabilities and cross-sections of the different atomic processes photon and electron scattering, photoionization, electron capture etc. QED corrections can be evaluated also to the different atomic properties in the external fields bound electron -factors and polarizabilities. In this review we will concentrate mainly on the corrections to the energy levels which are usually called the Lamb Shift (here the Lamb Shift should be understood in a more broad sense than the 2s, 2p level shift in a hydrogen). 

A question may arise whether there are non-QED corrections comparable in size with QED ones and thus preventing the direct tests of QED in atomic experiments. The most important among these corrections are nuclear ones. The nuclear recoil is usually included in QED theory of atoms ([9], [11], [12]). The nuclear size correction even dominates over the QED corrections in HCI 

In heavy atoms the nuclear uncertainty is still well below the electron correlation xmcertainty what allows for the evaluation of only the first-order in a QED corrections. 

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L. Labzowsky, I. Goidenko, QED theory of atoms, in P. Schwerdtfeger (Ed.), Relativistic Electronic Structure Theory, Part 1, Fundamentals, Elsevier, Netherlands, 2002, pp. 403-470. 

Labzowsky, L.N., Goidenko, 1. QED theory of atoms. In Schwerdtfeger, P. (ed.) Relativistic Electronic Stracture Theory, Part I, pp. 401-467. Elsevier, Amsterdam (2002)... 

The aim of this section is to extract from the measurements the values of the Rydberg constant and Lamb shifts. This analysis is detailed in the references [50,61], More details on the theory of atomic hydrogen can be found in several review articles [62,63,34], It is convenient to express the energy levels in hydrogen as the sum of three terms the first is the well known hyperfine interaction. The second, given by the Dirac equation for a particle with the reduced mass and by the first relativistic correction due to the recoil of the proton, is known exactly, apart from the uncertainties in the physical constants involved (mainly the Rydberg constant R0c). The third term is the Lamb shift, which contains all the other corrections, i.e. the QED corrections, the other relativistic corrections due to the proton recoil and the effect of the proton charge distribution. Consequently, to extract i oo from the accurate measurements one needs to know the Lamb shifts. For this analysis, the theoretical values of the Lamb shifts are sufficiently precise, except for those of the 15 and 2S levels. 

Symposia (Many-Body Theory of Atomic Systems, 1979, and Heavy-ion Spectroscopy and QED Effects in Atoms, 1992) and one ICAP conference (Gdteborg 1982). Ingvar has been an invited speaker and session chairman at innumerable scientific conferences all over the world. 

In this chapter, we present a rigorous formulation of the relativistic theory of atomic and molecular stmcture that is both simple and transparent. The resulting algorithms are fast and accurate, and require only modest computational resources, so that they constitute a new and powerful resource for quantum chemists. The formalism of QED is used to write down equations for the... 

There is a kind of atom where the nuclear effects are very large - exotic atoms, containing hadrons, i.e. particles that can interact strongly pions, antiprotons, kaons etc. In such atoms any advanced high-accurate QED theory is not necessary and a goal to study such atoms is to measure these nuclear parameters. An important feature of any spectroscopic measurement is its high accuracy in respect to non-spectroscopic methods. That is very important for exotic atoms, because some, like e.g. pionium (7r+7r -system or bound 7rp-system), are available in very small quantities (a few hundreds) [35],... 

Quantum-electrodynamics (QED) as the fundamental theory for electromagnetic interaction seems to be well understood. Numerous experiments in atomic physics as well as in high energy physics do not show any significant discrepancy between theoretical predictions and experimental results. The most striking example of agreement between theory and experiment represents the g factor of the free electron. The experimental value of g = 2.002 319 304 376 6 (87) [1] is confirmed by the calculated value of g = 2.002 319 304 307 0 (280) on the 10 11-level, where the fine structure constant as an input in the theoretical calculation was taken from the quantum Hall effect [2], Up to now uncalculated non-QED contributions play no important role. Indeed today experiment and theory of the free electron yield the most precise fine structure constant. 

The hyperfine splitting of the ground state of the hydrogen atom has been for a while one of the most precisely known physical quantities, however, its use for tests of QED theory is limited by a lack of our knowledge of the proton structure. The theoretical uncertainty due to that is on a level of 10 ppm. To go farther with theory we need to eliminate the influence of the nucleus. A few ways have been used (see e. g. [1]) ... 

Table 1. Comparison of the QED part of the theory to the experiment for hydrogen and deuterium atoms and for the 3He+ ion. The results are presented in kHz...

According to Primas (1991, p. 163), "the philosophical literature on reductionism is teeming with scientific nonsense," and he quotes, among others, Kemeny and Oppenheim (1956), who said "a great part of classical chemistry has been reduced to atomic physics." Perhaps it was not philosophers who invented this story after all. Almost certainly, Oppenheim and other philosophers of science at the time were familiar with the influential statements of Dirac, Heisenberg, Reichenbach, and Jordan on this issue. " Notoriously, the physicist Dirac (1929, p. 721) said, the underlying laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations which are too complicated to be soluble." Less famously, the philosopher of science Reichenbach (1978, p. 129) reiterated that "the problem of physics and chemistry appears finally to have been resolved today it is possible to say that chemistry is part of physics, just as much as thermodynamics or the theory of electricity." These views clearly stuck. For example, in a recent review of quantum electrodynamics (QED), to which Dirac made important contributions, the historian of science Schweber (1997, p. 177) says, "the laws of physics encompass in principle the phenomena and the laws of chemistry."... 

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