Uranium Lamb shift

As in the case of a hyperfine structure, there is a wealth of new experimental data on Lamb shift measurements of such exotic systems as lithium-like uranium U89+, again encouraging the relevant calculations [164-166],... 

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

To obtain the total binding energies, the (point-nucleus) Dirac eigenvalues of — 132279.92(1) eV for uranium and —101 581.37(1) eV for lead should be added to the Lamb-shift contribution quoted in Table 1.3. We may note, for example, that in... 

In Table 1.4 the individual contributions to the 2p i /2-2s transition energy in lithiumlike uranium are compiled. The one-electron QED-corrections are included as well. The predicted value of 280.46(9) 0.20 eV for the total Lamb shift is in agreement with the related experimental result of 280.59(10) eV (Schweppe et al. 1991). 

Fig. 1. Recent experimental results for the lsi/2 Lamb shift in hydrogenlike uranium. [3] - [6] correspond to the references. The dashed line indicates the current theoretical prediction [7].

The tabulated values were interpolated with a B-spline routine to provide numerical values for any nuclear charge number Z. We display these values in Fig. 11 together with the nonrelativistic reduced mass correction which is included in AErec- For uranium, the total effect to the lsi/2-state is 0.51 eV, including the nonrelativistic correction of 0.30 eV. Compared to the radiative effects discussed so far this might be thought tiny, but an experimental precision of better than 1 eV demands also for the proper calculation of Lamb shift contributions of this size of magnitude. 

Self energy and vacuum polarization of order a and the nuclear size account for the measured Lamb shift in hydrogenlike heavy ions at the current level of accuracy. Radiative corrections of the order contribute to the Lamb shift of the lsi/2 state and amount to about 1 eV for uranium. Facing higher precision in experiments, these corrections have to be evaluated to yield a reliable Lamb shift calculation. 

Table 1 Comparison of Za-expansion values to numerical calculcations including all orders in Za for a -order QED contributions to the Lamb shift of the lsi/2-state in lead and uranium. The Kalldn-Sabry contribution VPVP b) c) and the S(VP)E contribution are considered in the Uehling approximation only.

From the values given in the table below it is obvious that the finite nucleus and QED corrections contribute with the same order of magnitude to the Lamb shift in a heavy atom. The uncertainty in the theoretical value comes not only from yet uncalculated very high order QED contributions (estimated to be less few tenths of an eV) but also from less well known nuclear parameters of uranium that can amoimt to an uncertainty of about 0.3 eV. Up till now the best experimental value for the Is Lamb shift in obtained at the GSI [5] is 468 13 eV. This value is still an order of magnitude too imprecise to allow QED to be tested in high Coulomb fields where Za is not a small parameter. 

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). 

FIGURE 5.1 Various individual contributions to the ground-state Lamb shift in H-like uranium together with the experimental accuracies achieved so far [13-16], SE and VP denote the self energy and the vacuum polarisation contributions, respectively. 

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