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AMPD: EPS AMPD
AMPD 5: Sitzung 5
AMPD 5.4: Vortrag
Mittwoch, 4. April 2001, 10:55–11:20, H105
QED THEORY OF ATOMS AND IONS — •Leonti Labzowsky — StPetersburg State University, 198504 Uljanovskaya 1, Petrodvorets , StPetersburg, Russia
This Progress Report addresses the recent QED theory of atoms and ions. We concentrate here on the evaluation of the Lamb shift corrections where the achievments of the theory are most impressive. The most advanced QED theory is developed for the light hydrogenlike atoms. In this case the theory is based on the expansion in two parameters: fine structure constant α and the parameter α Z , where Z is the nuclear charge.
The lowest–order Lamb shift for H–like atoms has the order Δ ER(1,4) = m α (α Z)4 in relativistic units (atomic unit = m α2 r.u.), m is the electron mass. Now all the corrections Δ ER(n,l) = m(α)n(α Z)l with n = 2,3 and l = 4 are also known. The same is true for the contributions Δ ER(n,l) with n = 1, l = 5. The latest success of the theory was the completition of the evaluations of all contributions with n = 2, l = 5 [1,2]. The contributions with n = 2, l = 6 and n = 1, l = 7 are still incomplete. The whole situation with the Lamb shift for low–Z H–like atoms was reviewed recently in [3]. We would stress that there are reasons for which the straightforward evaluation of the energy of the excited states loses its sense at the certain level. The characteristics of the excited level by two parameters: energy E and width Γ is based on the resonance approximation for the process of the level excitation. The nonresonant (NR) corrections to the energy, first introduced by F.Low [4], are, in principle, process–dependent. The order of magnitude of NR corrections is formally m(α)2(α Z)6. However actually NR corrections contain small numerical factors and for the excitation of the Lyman–α transition 1s–2p in the process of Compton scattering reduce to 15 Hz [5].
The QED approach that avoids the expansion in α Z papameter and hence is applicable to the calculations in highly charged H–like ions was developed by Mohr [6] for the lowest-order electron self–energy and by Soff and Mohr [7] for the lowest-order vacuum polarization. Recently this method was applied also for the most accurate low–Z evaluations [8]. However this approach is not extended up to now to the next order α2 contributions for all Z values due to the lack of the most difficult second-order electron self–energy corrections. Recently the latter contribution was evaluated for H–like lead (Z = 82) and uranium (Z = 92) ions with relative accuracy about 12% [9].
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[5] L. N. Labzowsky, D. A. Solovyov, (unpublished).
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[8] U. Jentschura, P. J. Mohr and G. Soff, Phys. Rev. Lett. 82, 53 (1999).
[9] I. Goidenko, L. Labzowsky, A. Nefiodov, G. Plunien, G. Soff and S. Zschocke, Hyperfine Interactions, (accepted for publication).