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

Galina Pavlovna Anisimova; Igor Cheslavovich Mashek; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Robert Ivanovich Semenov; Martin Luther Tchoffo; Galina Aleksandrovna Tsygankova

doi:doi:10.11648/j.ajmp.20140304.11

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

Galina Pavlovna Anisimova, Igor Cheslavovich Mashek, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Robert Ivanovich Semenov, Martin Luther Tchoffo, Galina Aleksandrovna Tsygankova

Published in American Journal of Modern Physics (Volume 3, Issue 4)

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.

Published in	American Journal of Modern Physics (Volume 3, Issue 4)
DOI	10.11648/j.ajmp.20140304.11
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), 2014. 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.

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APA Style

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://article.sciencepublishinggroup.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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Author Information

Galina Pavlovna Anisimova

Saint-Petersburg State University, Saint-Petersburg, Russian Federation
Igor Cheslavovich Mashek

Saint-Petersburg State University, Saint-Petersburg, Russian Federation
Olga Aleksandrovna Dolmatova

Saint-Petersburg State University, Saint-Petersburg, Russian Federation
Anna Petrovna Gorbenko

Saint-Petersburg State University, Saint-Petersburg, Russian Federation
Robert Ivanovich Semenov

Saint-Petersburg State University, Saint-Petersburg, Russian Federation
Martin Luther Tchoffo

University of Dschang, Po Dschang, Cameroon
Galina Aleksandrovna Tsygankova

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

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APA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

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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