Quantum Electrodynamical Corrections in Critical Fields

Abstract

We investigate field-theoretical corrections, such as vacuum polarization and self energy to study their influence on strongly bound electrons in heavy and superheavy atoms. In critical fields (Z ≃ 170) for spontaneous e+e−pair creation the coupling constant of the external field Zα exceeds 1 thereby preventing the ordinary perturbative approach of quantum electrodynamical corrections which employs an expansion in Zα. For heavy and superheavy elements radiative corrections have to be treated to all orders in Zα. The Feynman diagrams for the lowest-order (a) vacuum polarization and (b) self energy are displayed in Fig. 1. The double lines indicate the exact propagators and wave functions in the Coulomb field of an extended nucleus. Fig. 2 shows an Zα -expansion of the vacuum polarization graph. The dominant effect is provided by the Uehling contribution being visualized by the first diagram on the right hand side. It is linear in the external field and thus of order α(Zα).