TY - JOUR T1 - Relativistic Theory of One- and Two Electron Systems: Valley of Stability in the Helium-Like Ions AU - I. Sakho JO - Journal of Atomic and Molecular Sciences VL - 1 SP - 23 EP - 40 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/10.4208/jams.012511.030111a UR - https://global-sci.org/intro/article_detail/jams/8270.html KW - screening constant, hydrogen-like ions, helium-like ions, valley of stability. AB -

A semi-relativistic total energy of the hydrogen-like ions is presented. The established 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. Comparison 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 constant $\sigma^{\text{rel}}$ decreases when increasing the nuclear charge up to $Z = 5.$ Beyond, $\sigma^{\text{rel}}$ increases when increasing $Z$ and, the plot $\sigma^{\text{rel}} = f (Z)$ 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 $C^{4+},$ $N^{5+},$ $O^{6+},$ $F^{7+},$ $Ne^{8+},$ $\cdots,$ can only exist in hot laboratory and astrophysical plasmas.