Hydrogen-like ions Lamb shift

Table 1. Lamb shift in mid-Z hydrogen-like ions...

In contrast to the study of the Lamb shift and hyperfme structure, it is possible to perform experiments on the g factor of the bound electron in different hydrogen-like ions with about the same accuracy. The experiment [1] is now in progress and some other hydrogen-like ions can be measured soon. This provides a possibility to learn about the bound g factor as a function of the nuclear charge Z and the nuclear mass number A. The ions under study [1] must have spinless nuclei and so they have the most simple level scheme. 

All previous 2S Lamb shift measurements for medium-Z hydrogen-like ions have been carried out using fast ion beams, and uncertainties associated with Doppler shifts form a significant source of error in all these experiments. Various methods have been employed or suggested for reducing the sensitivity of fast beam experiments to Doppler corrections [22]—[24]. A measurement of the 2S1/2-2P3/2 transition frequency in N6+ using a fast ion beam is currently under way at Florida State University [25]. Our approach, however, is to reduce such... 

In this paper, we summarise our progress towards Is Lamb shift measurements on medium Z hydrogen-like ions produced in an electron beam ion trap (EBIT), where the X-ray emission is free from the problems of satellite contamination and Doppler shifts. In this context, we note that a measurement of the Is Lamb shift in hydrogen-like Mg11+ has been performed at the Livermore EBIT using a quasimonolithic crystal setup, and reaching a precision of 13% for the Lamb shift dominated by counting statistics [14]. With our setup, the... 

Recently, in addition to the Lamb shift [26] and hyperfine structure, one more value was measured with a high accuracy - the g factor of an electron bound in a hydrogen-like ion [27]. 

Figure 2. The three dominant contributions to the slowly varying function F 2s,aZ) for the Lamb shift of 2s states of highly-charged hydrogen-like ions self-energy, vacuum polarization, and finite nuclear size, are given along the isoelectronic sequence.

Extensive calculations of hydrogen-like ions were made by Johnson and Soff [13], seven contributions to the Lamb shift being analyzed and their accuracy being estimated. This work references many earlier studies and the energy levels predicted for the three ions are (all in cm"" ) ... 

Extensive calculations of hydrogen-like ions by Johnson and Soff [21] describe seven contributions to the Lamb shift and their accuracy. The binding energy of Is /g four lowest energy levels (in 10 cm ) are reprinted from this work which references earlier contributions to one-electron atoms ... 

In Tables 4,5 we summarize all known corrections to the ground-state energy of hydrogen-like U and Pb ions including the complete set of the SESE corrections obtained in the present paper. The inaccuracy assigned to our results for SESE a) (red) + SESE b), c) corrections remains the main source of the total error in the theoretical Lamb shift prediction. We expect that the inaccuracy can be essentially diminished within the framework of the method described above. 

T. Stohlker et al. The Is Lamb Shift in Hydrogen-like Uranium Measured on Cooled, Decelerated Ion Beams, submitted to Phys. Rev. Lett. 

Our target is to develop a theory for the Lamb shift and the fine structure in these two atomic systems. Eventually we need to determine the 2s — 2pi/2 splitting in the helium ion (for comparison with the experiment [6]), difference of the Lamb shifts ER(2s) — ER(3s) in 4He+ (for the project [7]) and the 2p3/2 — 2s interval in hydrogen-like nitrogen. The difference mentioned is necessary [12,1] if one needs to compare the results of the Lamb shift (n = 2) measurement [6] and the 2s — 3s experiment. 

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). 

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