Relativistic Theory of One- and Two Electron Systems: Valley of Stability in the Helium-Like Ions

doi:10.4208/jams.012511.030111a

Relativistic Theory of One- and Two Electron Systems: Valley of Stability in the Helium-Like Ions

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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

Pages: 18

Keywords: screening constant hydrogen-like ions helium-like ions valley of stability.

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Bibliography

2018
https://doi.org/10.1002/9781119476948.biblio [Citations: 0]

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