@Article{JAMS-3-23,
author = {I. Sakho},
title = {Relativistic Theory of One- and Two Electron Systems: Valley of Stability in the Helium-Like Ions},
journal = {Journal of Atomic and Molecular Sciences},
year = {2012},
volume = {3},
number = {1},
pages = {23--40},
abstract = {<p style="text-align: justify;">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&#39;s semi-classical formula. Comparison with relativistic total energy expression obtained from the Dirac&#39;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.</p>},
issn = {2079-7346},
doi = {https://doi.org/10.4208/jams.012511.030111a},
url = {http://global-sci.org/intro/article_detail/jams/8270.html}
}