Year: 2012
Journal of Atomic and Molecular Sciences, Vol. 3 (2012), Iss. 1 : pp. 23–40
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jams.012511.030111a
Journal of Atomic and Molecular Sciences, Vol. 3 (2012), Iss. 1 : pp. 23–40
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: screening constant hydrogen-like ions helium-like ions valley of stability.
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