Energy approach for definition of the Lamb shift self-energy part

An advanced method for calculation of the self-energy part of the Lamb shift LE is presented. In an atomic system the radiative shift and the relativistic part of the energy are, in. principle, determined by one and the same physical field [1]. It may be supposed that there exists some universal function that connects the self -energy correction and the relativistic energy. The self-energy correc¬tion for the states of a hydrogen-like ion was presented by Mohr [2]. We construct the similar universal function F but which it is correct for any multi-electron system. The procedure of generalization for a case of multi-electron system with the finite nucleus consists of the following steps: 1). Calculation of the relativistic energy values for the states nlj of H-like ions with the point nucleus (in accordance with the Zommerfeld formula); 2). Construction of an approximating universal function F; 3). Calculation of the relativistic energy values for the states nlj of multi-electron system with the finite nucleus; 4). Calculation of LE for the cited states. The energies of the states nlj of multi-electron system are calculated twice: with a conventional constant of the fine structure alpha=1/137.04 and with alpha1=alpha/1000. The results of latter calculations were considered as non-relativistic. This permitted isolation of ER and .

References:
1. A.V. Glushkov, Relativistic Quantum Theory, Odessa, Astroprint (2008).-900 P.
2. A. Glushkov, O. Khetselius, L. Lovett, A. Loboda, D. Sukharev, Int. J. Quant. Ch., 109 (2009) 1617-1624.