Model-QED operator for superheavy elements

Abstract

The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges 110 Z 170. The self-energy part of the model operator is represented by a nonlocal potential based on diagonal and off-diagonal matrix elements of the ab initio self-energy operator with the Dirac-Coulomb wave functions. The vacuum-polarization part consists of the Uehling contribution which is readily computed for an arbitrary nuclear-charge distribution and the Wichmann-Kroll contribution represented in terms of matrix elements similarly to the self-energy part. Performance of the method is studied by comparing the model-QED-operator predictions with the results of ab initio calculations. The model-QED operator can be conveniently incorporated in any numerical approach based on the Dirac-Coulomb-Breit Hamiltonian to account for the QED effects in a wide variety of superheavy elements.

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

“…Reference [383] contains the values of F (1) n,κ (Zα) for nd 3/2 to ng 9/2 up to n = 5 for a point nucleus. The finite size of correction for 2s states and 2p 1/2 states can be found in [142,143,378] for 26 ≤ Z ≤ 100, for 10 ≤ Z ≤ 120 in [68] and for 100 ≤ Z ≤ 170 in [340]. The comparison between different theoretical values with and without finite size correction for 2s, 2p 1/2 and 2p 3/2 states is shown in Fig.…”

“…It was followed by the calculation of the self-energy contribution of the 1s 1/2 level for finite nuclei up to Z = 170 [339]. This evaluation has recently been extended to all states up to n = 5 and J = 5/2 [340]. The method described in Ref.…”

“…The work from Ref. [68] has been extended recently to Z = 170 [340]. In both works, the selfenergy for a given Z value is calculated for a specific nuclear size, using the Fermi model.…”

“…The Welton approximation [414] was introduced in the MDFGME code in 1987 [65] for s-states and generalized to ≥ 0 in [66]. Effective operators directly based on BSQED have been introduced more recently [68,340].…”

“…A recent extension to superheavy elements up to nuclear charge Z = 170 has been carried out in Ref. [340]. This scheme gives very accurate results for the self-energy.…”