QED effects

DCB is correct to second order in the fine-structure constant a, and is expected to be highly accurate for all neutral and weakly-ionized atoms [8]. Higher quantum electrodynamic (QED) terms are required for strongly-ionized species these are outside the scope of this chapter. A comprehensive discussion of higher QED effects and other aspects of relativistic atomic physics may be found in the proceedings of the 1988 Santa Barbara program [9]. 

I. Lindgren, I. Martinson and R. Schuch (eds). Heavy-Ion Spectroscopy and QED Effects in Atomic Systems (Proceedings of Nobel Symposium 85, Saltsjobaden, Sweden, June 29 - July 3, 1992), Physica Scripta, T46 (1993). 

Recent progress in the study of high- and medium-Z ions [26,27] make calculations of two-loop corrections an important problem and that involves more QED effects in the study and now the status of high-Z and low-Z physics is very similar both need to take into account a2 terms and both cannot only apply an expansion in Za. 

The measured hyperfine splittings of 2 3Pi level were in reasonable agreement with the relativistic calculations of [96], and also with non-relativistic calculations corrected for relativistic and QED effects [114,115], The results for the hyperfine corrected 21S o — 23Pl interval in 14N5+ are compared with theory in table 3. QED corrections make up 3.5% of the measured interval. The experiment is hence sensitive to these corrections at the level of 20 ppm, the highest precision for a Lamb shift in any multiply-charged ion. 

Obtaining experimental tests of the theory of hydrogen-like ions at moderate Z is challenging. Except for hydrogen there appear to be no measurements more precise than current theory. In the next decade, small but significant improvements in precision can be expected for Z = 2, 7 and 14. For moderate-.Z helium-like ions, laser techniques probe relativistic QED effects at higher precision than... 

After the corrections for the pressure shifts Torii et al. [18] obtained wavelengths in vacuum, which revealed a small discrepancies of several ppm, as shown in Fig. 6. The theoretical values are further corrected for QED effects [9,19,20], yielding excellent agreements to ppm precision. Various QED corrections calculated by Korobov [21] are itemized in Table 1. 

Table 1. Known theoretical contributions to the gj factor of an electron bound in the ground state of 12C5+. All values axe given in units of 10 9. The error estimates are discussed in the text. If no error is given, it is less than 0.5 x 10-10. The errors for the total value axe due to the (Za) expansion fox the xecoil contxibution, the numerical uncertainties for the QED effects of order (a/ir), and the estimated error for the bound-state QED contribution of order (a/7r)2. In order not to underestimate any systematic effect, the numerical errors were linearly added...

The Lamb shift is mainly a QED effect, perturbed by the influence of the nuclear structure... 

In the case of the recent experiment with hydrogen-like carbon the nontrivial QED effects contribute an observable amount (see Table 1). We need to mention that, due to some delay of the final publications of the experimental result [1] and theoretical calculations [10], no actual theoretical predictions have been published. Most of the presentations (conference and seminar talks and posters) dealt with unaccurate theoretical predictions because it was believed that nothing had been known on the two-loop corrections. However, that was not the case, because from the beginning of the theoretical calculations up to recent re-calculations it was clearly stated ed [6] that the (Za)2 term in Eq. (4) is of pure kinematic origin and so the result is valid in any order of the expansion in a for the anomalous magnetic moment of a free electron, and in particular... 

A selection of experimental measurements across medium Z helium-like resonances is shown in Table 3 and compared with recent theory. The most precise absolute measurement is attributed to Deslattes and co-workers [33] with a 12 ppm measurement of the w transition in argon. Our methodology is similar to that of Deslattes et al. in the use of an external X-ray calibration standard lying close to the wavelength of interest. The recoil-ion experimental method used therein also eliminates the need for Doppler corrections and uncertainties in that work as in our EBIT experiment. Argon is at the lower end of the medium Z elements where QED effects are smaller relative to the transition energies. However, this very precise measurement lies below all recent theoretical calculations shown in Table 3. 

An interesting problem is the precise calculation and measurement of the Lamb shift 6 which we describe here, commenting on the main points of interest. First, there is a disparity - not yet accounted for - both between the at present most precisely known theoretical values of S, as well as between experiment and theory. Another important point is the opportunity provided to obtain information on the structure and properties of corrections which are not given directly by QED. In contrast to the anomalous magnetic moment, the Lamb shift characterizes the properties of bound electrons, i.e. it takes account of not only the QED effects but the effects arising from the nuclear structure. If the corrections independent of QED are far beyond the error limits of measurements for an anomalous magnetic moment, the corrections... 

The main significance of the work so far carried out at Oxford is that it demonstrates the feasibility of making measurements of the IS - 2S transition with a frequency doubled cw system. This opens the way to considerable improvements in precision, but the interpretation of the measurements will depend on what other information is available - the transition frequency is sensitive to QED effects, the proton size, and the values of fundamental constants. Cynics might point out that after well over a decade of work on the IS - 2S transition, the results have produced no real surprises. A more optimistic view is that it is only over the last year or two that it has become possible to study the transition with the standard techniques of high resolution cw laser spectroscopy, and the next decade will bring dramatic developments. We shall see. 

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