QED radiative corrections and many-body effects in atoms: vacuum polarization and binding energy shifts in alkali metals

Abstract

We calculate vacuum polarization corrections to the binding energies in neutral alkali atoms Na through to the superheavy element E119. We employ the relativistic Hartree-Fock method to demonstrate the importance of relaxation of the electronic core and the correlation potential method to study the effects of second and higher orders of perturbation theory. These many-body effects are sizeable for all orbitals, though particularly important for orbitals with angular momentum quantum number l > 0. The orders of magnitude enhancement for d waves produces shifts that, for Rb and the heavier elements, are larger than those for p waves and only an order of magnitude smaller than the s-wave shifts. The many-body enhancement mechanisms that operate for vacuum polarization apply also to the larger self-energy corrections.

Atomic many-body effects and Lamb shifts in alkali metals

“…We have introduced an l dependence into the electric part of the radiative potential, which enables the d-level shifts to be controlled and the overall accuracy of the potential improved. The many-body enhancement mechanisms that we have observed in this work for the self-energy are the same that we saw in our recent work on the vacuum polarization (Uehling) shifts [30].…”

“…The corrections for s levels enter at around 5%. While the relaxation effect increases the size of the s-wave self-energy shift for the lighter atoms Na to Cs, interestingly (unlike what we observed for the vacuum polarization [30]) it decreases the size of the shift for Fr and E119.…”

“…In the current paper we focus on the self-energy aspect of the problem. We addressed in detail many-body effects on the dominant contribution to the vacuum polarization (the Uehling potential) in our recent paper [30].…”

“…Using the ratio methods above, one may yield reasonable estimates for the self-energy corrections for valence s orbitals of atoms and ions. However, for estimating shifts for orbitals with l > 0, this procedure may prove to be cumbersome or inadequate, since core relaxation corrections determine the size and the sign of the effect [8,30,33].…”

“…It is a simple matter to include the electric parts of the radiative potential in the atomic structure codes. They may be added to the Hartree-Fock or the nuclear potential, as is done for Uehling [30,33]. Inclusion of the (off-diagonal) magnetic part of the radiative potential is more involved and the Dirac equations must be modified accordingly,…”