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

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

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

  1. On maximal acceleration and quantum acceleratum operator in quantum mechanics

    El-Nabulsi, Rami Ahmad

    Quantum Studies: Mathematics and Foundations, Vol. 5 (2018), Iss. 4 P.543

    https://doi.org/10.1007/s40509-017-0142-x [Citations: 16]
  2. The stark effect on the spectrum energy of tritium in first excited state with relativistic condition

    Prastowo, S H B | Supriadi, B | Bahri, S | Ridlo, Z R

    Journal of Physics: Conference Series, Vol. 1008 (2018), Iss. P.012013

    https://doi.org/10.1088/1742-6596/1008/1/012013 [Citations: 0]
  3. Screening Constant by Unit Nuclear Charge Method

    Bibliography

    2018

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