QED calculations in heavy many-electron atoms and one-electron quasi-molecules

Construction of simple one-electron approach to one-loop QED operator is an important task for the relativistic quantum theory of atoms and molecules. In this work we used two modifications [1,2] of the model QED potential approach to calculations of the Lamb shift in many-electron atoms and one-electron quasi-molecules. The model potential is constructed as a sum of local and nonlocal (separable) potentials. The nonlocal part of the model potential was introduced to reproduce exactly the diagonal elements [2] and also off-diagonal elements [1] of the one-loop {ab initio} QED operator. The one-particle model QED operator was introduced in the Dirac-Fock and CI+MBPT relativistic calculations of the heavy and super-heavy atoms and in the calculations of the diatomic quasi-molecules. The comparison of the data obtained in different approaches to the one-loop QED operator is presented. Model QED potential is applied to calculate Lamb shift in the U$^{91+}$-U$^{92+}$ dimer. The results are compared with Ref. [3].\\ {[1]} V.M. Shabaev, I.I. Tupitsyn, and V.A. Yerokhin, Phys.~Rev.~A {\bf 88}, 012513 (2013).\\ {[2]} I.I. Tupitsyn and E.V. Berseneva, Opt. Spectrosc. {\bf 114}, 682, (2013).\\{[3]} A.N. Artemyev and A. Surzhykov, Phys.~Rev.~Lett. {\bf 114}, 243004 (2015).