American Journal of Modern Physics

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The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom

Received: 28 May 2014    Accepted: 29 May 2014    Published: 20 June 2014
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Abstract

By the semiempirical method in the intermediate coupling, the fine-structure parameters of 1sni Helium atom configurations were determined from the resolution of the system of nonlinear equations by the Newton’s iteration method. The system is based on an energy operator nondiagonal matrix, in which the following interactions were taken into account: the electrostatic, the spin-orbit (own and other) and the spin-spin interactions. With the obtained fine-structure parameters, the numerical diagonalization of the energy operator matrix was effected. The result was the calculated energies, coinciding to last digit with the experimental analogues, and the intermediate coupling coefficients. The gyromagnetic ratios of the 3I6 and 1I6 levels were determined and the appreciation of the character of the coupling in the consider systems was done. The Zeeman structure of the 1sni configurations was investigated. Its particularity and the domain of linearity of the magnetic field were determined. The gyromagnetic ratios of all the four configurations levels were calculated by the magnetic component splitting.

DOI 10.11648/j.ajmp.20140304.11
Published in American Journal of Modern Physics (Volume 3, Issue 4, July 2014)
Page(s) 143-151
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Energy Operator Matrix, LSJM Representation, Uncoupled Moments Representation, Zeeman Splitting, Magnetic Field, Crossing and Anticrossings of the Magnetic Sublevels

References
[1] NIST Atomic Spectra Database Levels Data, 2009.
[2] NIST ASD Levels Output, 2013.
[3] A.P.Yutsis, and A.Yu.Savukinas, Mathematical Foundations of the Atomic Theory, Vil`nyus, 1973 [in Russian].
[4] D.A.Varshalovich, A.N.Moskalev, and V.K.Khersonskii, Quan-tum Theory of the Angular Moment, Leningrad, 1975.
[5] I.I.Sobelman, Introduction to the Theory of Atomic Specters, Moscow, 1963 [in Russian].
[6] J.B.Green, and J.F.Eichelberger, Phys.Rev., 56 (1), 51, 1939.
[7] G.P.Anisimova, O.A.Dolmatova, A.P.Gorbenko, and M.Choffo, American Journal of Modern Physics, 2 (6), 334, 2013.
[8] V.Kaufman, and J.Sugar, J. Phys. Chem. Rev. Data, 17 (4), 1679, 1988.
Author Information
  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

  • University of Dschang, Po Dschang, Cameroon

  • Saint-Petersburg State University, Saint-Petersburg, Russian Federation

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    Galina Pavlovna Anisimova, Igor Cheslavovich Mashek, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Robert Ivanovich Semenov, et al. (2014). The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom. American Journal of Modern Physics, 3(4), 143-151. https://doi.org/10.11648/j.ajmp.20140304.11

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    ACS Style

    Galina Pavlovna Anisimova; Igor Cheslavovich Mashek; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Robert Ivanovich Semenov, et al. The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom. Am. J. Mod. Phys. 2014, 3(4), 143-151. doi: 10.11648/j.ajmp.20140304.11

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    AMA Style

    Galina Pavlovna Anisimova, Igor Cheslavovich Mashek, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Robert Ivanovich Semenov, et al. The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom. Am J Mod Phys. 2014;3(4):143-151. doi: 10.11648/j.ajmp.20140304.11

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  • @article{10.11648/j.ajmp.20140304.11,
      author = {Galina Pavlovna Anisimova and Igor Cheslavovich Mashek and Olga Aleksandrovna Dolmatova and Anna Petrovna Gorbenko and Robert Ivanovich Semenov and Martin Luther Tchoffo and Galina Aleksandrovna Tsygankova},
      title = {The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom},
      journal = {American Journal of Modern Physics},
      volume = {3},
      number = {4},
      pages = {143-151},
      doi = {10.11648/j.ajmp.20140304.11},
      url = {https://doi.org/10.11648/j.ajmp.20140304.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.20140304.11},
      abstract = {By the semiempirical method in the intermediate coupling, the fine-structure parameters of 1sni Helium atom configurations were determined from the resolution of the system of nonlinear equations by the Newton’s iteration method. The system is based on an energy operator nondiagonal matrix, in which the following interactions were taken into account: the electrostatic, the spin-orbit (own and other) and the spin-spin interactions. With the obtained fine-structure parameters, the numerical diagonalization of the energy operator matrix was effected. The result was the calculated energies, coinciding to last digit with the experimental analogues, and the intermediate coupling coefficients. The gyromagnetic ratios of the 3I6 and 1I6 levels were determined and the appreciation of the character of the coupling in the consider systems was done. The Zeeman structure of the 1sni configurations was investigated. Its particularity and the domain of linearity of the magnetic field were determined. The gyromagnetic ratios of all the four configurations levels were calculated by the magnetic component splitting.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - The Fine-Structure Parameters and Zeeman Splitting of Levels of the Configurations 1sni (n = 7 − 10) of the Helium Atom
    AU  - Galina Pavlovna Anisimova
    AU  - Igor Cheslavovich Mashek
    AU  - Olga Aleksandrovna Dolmatova
    AU  - Anna Petrovna Gorbenko
    AU  - Robert Ivanovich Semenov
    AU  - Martin Luther Tchoffo
    AU  - Galina Aleksandrovna Tsygankova
    Y1  - 2014/06/20
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajmp.20140304.11
    DO  - 10.11648/j.ajmp.20140304.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 143
    EP  - 151
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20140304.11
    AB  - By the semiempirical method in the intermediate coupling, the fine-structure parameters of 1sni Helium atom configurations were determined from the resolution of the system of nonlinear equations by the Newton’s iteration method. The system is based on an energy operator nondiagonal matrix, in which the following interactions were taken into account: the electrostatic, the spin-orbit (own and other) and the spin-spin interactions. With the obtained fine-structure parameters, the numerical diagonalization of the energy operator matrix was effected. The result was the calculated energies, coinciding to last digit with the experimental analogues, and the intermediate coupling coefficients. The gyromagnetic ratios of the 3I6 and 1I6 levels were determined and the appreciation of the character of the coupling in the consider systems was done. The Zeeman structure of the 1sni configurations was investigated. Its particularity and the domain of linearity of the magnetic field were determined. The gyromagnetic ratios of all the four configurations levels were calculated by the magnetic component splitting.
    VL  - 3
    IS  - 4
    ER  - 

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