Self-energy-corrected Dirac wave functions for advanced QED calculations in highly charged ions

Abstract

The procedure for the calculation of the self-energy-corrected wave function of the bound electron in the field of the nucleus is discussed. We present the related formulas and discuss the numerical difficulties and the methods used to overcome them. The results of the calculation are presented for a wide range of ions. Possible applications of the numerically obtained wave functions are discussed.

Vacuum polarization and finite nuclear size effects in the two-photon decay of hydrogen-like ions

“…The total rates W E1,E1 for this 2E1 transition are displayed in Table II for nuclear charges ranging from Z = 1 to Z = 92 and for different electron-nucleus interaction potentials. In particular, calculations have been performed for the pointlike and finite-size nucleus and by accounting the vacuum polarization as described by the Uehling potential (28). Moreover, by following the well-known non-relativistic Z-behaviour [34], we present our results divided by Z 6 .…”

“…Apart from the finite nuclear size effects, other phenomena can also influence the two-photon decay rate of hydrogen-like ions. For example, the interaction of the electron with the quantum vacuum may affect the wavefunctions [27,28], the energy levels [25], and the transition operators [11][12][13] and, hence, the decay rate. In the one-loop approximation, two QED contributions are usually considered: vacuum polarization and self energy.…”

Radiative and photon-exchange corrections to New Physics contributions to energy levels in few-electron ions

“…Using the angular decomposition of I (ω), as was done for instance in Refs. [33,34], and performing the angular integration in Eq. ( 5b) analytically, we obtain…”

“…and R J (abcd, ω) and R J (abcd, ω) are the generalized Slater radial integral given explicitly in Refs. [33,34] and its derivative w.r.t. ω, respectively.…”

“…A method has been developed for the challenging numerical computation of the SE-corrected wave functions, and described in detail in Ref. [34]. We use the codes and results developed in that work, for our present calculations.…”