Abstract
A semi-relativistic total energy of the hydrogen-like ions is presented. The es- tablished expression taking only into account the dependence of the mass electron on the speed could be considered as a first correction of the Bohr's semi-classical formula. Com- parison with relativistic total energy expression obtained from the Dirac's relativistic wave equation is made. In addition, the present relativistic theory of the hydrogen- like ions is extended to the helium isoelectronic series. It is shown that, for the ground state of two electron systems, the relativistic screening constantσ rel decreases when increasing the nu- clear charge up to Z=5. Beyond,σ rel increases when increasing Z and, the plotσ rel = f (Z) is like a valley of stability where the bottom is occupied by the B 3+ -helium-like ion. As a result, only He, Li + , Be 2+ and B 3+ exist in the natural matter in low temperature. All the other helium-like positive-ions, such as C 4+ , N 5+ , O 6+ , F 7+ , Ne 8+ ,��� , can only exist in hot
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