Issues related to the problem of convergence of the series of the perturbation theory in the quasipotential approach are considered. New fine structure constant logarithmic contributions to the fine shift of the energy levels, vanishing in the limit m2 rightarrow m1 are discussed.
The analysis of results of researches of value of the fine shift of the energy levels with an accuracy up to sixth order on
the fine structure constant shows, that the fullest information on this problem gives the quasipotential approach. On the
basis of a quasipotential method have been analysed two-photon Coulomb exchanges and new value of fine shift of the
energy levels of hydrogen-like atom has been established.
Precise calculation of corrections to the fine shift of the energy levels is possible only if the quantities of the type (equation available in manuscript) are absent in the terms of the perturbation theory in the fine structure constant. An attempt to find the method of Coulomb interaction description of the hydrogen-like atoms is realized in this paper. We obtained the correction (equation available in manuscript) which was earlier unknown.
The modification of quasipotential approach to the investigation of binding effects on the fine shift of energy levels of
hydrogen-like atoms is applied. The results provide a step towards better agreement between the relativitic calculations of
hydrogen-like systems and high-precision spectroscopic measurements.
The problem of the application of different gauges for calculation of the fine shift of the S energy levels in the hydrogen-like atoms is considering up.
A new method of calculation of the values the fine shifts of energy levels of bound states is considered basing on the upgraded relativistic quasipotential equation. The appropriate perturbation theory permitting to calculate the shifts of the energy levels in hydrogen-like atoms with high accuracy is developed. The new logarithmic corrections of the order (alpha) 4ln(beta) -1, (alpha) 5(beta) 2Ln(beta) -1 are obtained and earlier results are confirmed.
The effect of recoil on the fine shift of the energy levels of the hydrogen-like atom is considered up to terms of the order (alpha) 6(mu) 3/(m1m2)(Beta) ln(Beta) -1. Contributions of this order from one-photon exchange between particles with unequal masses (m1 not equal to m2) are calculated analytically for the first time.
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