Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Martin Tchoffo

doi:doi:10.11648/j.ajmp.20130206.20

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Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Martin Tchoffo

Published in American Journal of Modern Physics (Volume 2, Issue 6)

Received: 5 October 2013 Accepted: Published: 10 November 2013

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Abstract

In the energy operator matrix of four-level configurations with s and i -electrons in external shells, we take into account the following magnetic interactions: spin-other-orbit, spin-spin, and orbit-orbit interactions. The calculation of matrix elements is done in the uncoupled moments representation with subsequent translation (passage) to the LSJM- representation. Comparison with independent calculations in LSJM-representation for and configurations is done. The method of calculation in electronic configuration is extended to the holes configurations i^25 s As results the energy operator matrix is complemented with new physical conditions on radial integrals of Marvin’s spin interactions, which permits to ameliorate the precision of future calculations of fine structure parameters by semi-empirical methods.

Published in	American Journal of Modern Physics (Volume 2, Issue 6)
DOI	10.11648/j.ajmp.20130206.20
Page(s)	334-340
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

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References

[1]	NIST Atomic Spectra Database Levels Data. 2008.
[2]	Yutsis A.P., Savukinas A.Yu. Mathematical basis of atom theory (in Russian) Vilnius, 1973, 479 P.
[3]	Anisimova G.P., Kapel’kina E.L. "Orbit-orbit interaction in two electronic matrix energy operator of configurations with p and s electrons". Optics and spectroscopy. 1999. T. 87, №6, pp.885-892.
[4]	Anisimova G.P., Efremova E.A., Tsygankova G.A., Tsygankov M.A. "Calculation of fine and Zeeman structure of configuration 2npnd+2p(n+1)s of a carbon atom by semi empirical method," Vestnik of Saint-Petersburg State University, ser.4, issue 36, 2007, pp. 49-60.
[5]	Sobelman I.I. Introduction to the theory of atomic specters. (in Russian) M. 1963, 640 p.
[6]	Varshalovich D.A., Moscalev A.H., Hersonski V.K. Quantum theory of angular momenta. (in Russian) L., 1975, 439 P.
[7]	Kondon E., Shortly G. Theory of atomics specters. (in Russian) M. 1949, 440 p.
[8]	Anisimova G.P., Semenov R.I., Tuchkin V.I. Optics and spectroscopy 1996. T. 80. N4 PP.544-556.
[9]	Anisimova G.P., Semenov R.I., Tuchkin V.I. Optics and spectroscopy 1996. T. 76. N5 PP. 720-725.
[10]	Anisimova G.P., Kapel’kina E.L. "Spin-other-orbit interaction in two electronic matrix energy operator of configurations with p and s electrons. Direct terms". Optics and spectroscopy. 1998.T. 84,n3, pp.364-368.
[11]	Anisimova G.P., Semenov R.I., Tuchkin V.I. Optics and spectroscopy 1994. T. 77. N5 PP. 695-699.
[12]	Anisimova G.P., Kapel’kina E.L. "The account of spin-spin interaction in the energy matrices of the two electrons configurations with p and s electrons". Optics and spectroscopy. 1999.T. 87,n1, pp.15-21.

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Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Martin Tchoffo. (2013). Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. American Journal of Modern Physics, 2(6), 334-340. https://doi.org/10.11648/j.ajmp.20130206.20

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ACS Style

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Martin Tchoffo. Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. Am. J. Mod. Phys. 2013, 2(6), 334-340. doi: 10.11648/j.ajmp.20130206.20

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AMA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Martin Tchoffo. Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. Am J Mod Phys. 2013;2(6):334-340. doi: 10.11648/j.ajmp.20130206.20

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@article{10.11648/j.ajmp.20130206.20,
  author = {Galina Pavlovna Anisimova and Olga Aleksandrovna Dolmatova and Anna Petrovna Gorbenko and Martin Tchoffo},
  title = {Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells},
  journal = {American Journal of Modern Physics},
  volume = {2},
  number = {6},
  pages = {334-340},
  doi = {10.11648/j.ajmp.20130206.20},
  url = {https://doi.org/10.11648/j.ajmp.20130206.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130206.20},
  abstract = {In the energy operator matrix of four-level configurations with s and i -electrons in external shells, we take into account the following magnetic interactions: spin-other-orbit, spin-spin, and orbit-orbit interactions. The calculation of matrix elements is done in the uncoupled moments representation with subsequent translation (passage) to the LSJM- representation. Comparison with independent calculations in LSJM-representation for and configurations is done. The method of calculation in electronic configuration is extended to the holes configurations i^25 s As results the energy operator matrix is complemented with new physical conditions on radial integrals of Marvin’s spin interactions, which permits to ameliorate the precision of future calculations of fine structure parameters by semi-empirical methods.},
 year = {2013}
}

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TY  - JOUR
T1  - Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells
AU  - Galina Pavlovna Anisimova
AU  - Olga Aleksandrovna Dolmatova
AU  - Anna Petrovna Gorbenko
AU  - Martin Tchoffo
Y1  - 2013/11/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130206.20
DO  - 10.11648/j.ajmp.20130206.20
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 334
EP  - 340
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20130206.20
AB  - In the energy operator matrix of four-level configurations with s and i -electrons in external shells, we take into account the following magnetic interactions: spin-other-orbit, spin-spin, and orbit-orbit interactions. The calculation of matrix elements is done in the uncoupled moments representation with subsequent translation (passage) to the LSJM- representation. Comparison with independent calculations in LSJM-representation for and configurations is done. The method of calculation in electronic configuration is extended to the holes configurations i^25 s As results the energy operator matrix is complemented with new physical conditions on radial integrals of Marvin’s spin interactions, which permits to ameliorate the precision of future calculations of fine structure parameters by semi-empirical methods.
VL  - 2
IS  - 6
ER  -

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Author Information

Galina Pavlovna Anisimova

Saint -Petersburg State University, Faculty of Physics, 198504, Stary Peterhof, Saint-Petersburg, Russian Federation
Olga Aleksandrovna Dolmatova

Saint -Petersburg State University, Faculty of Physics, 198504, Stary Peterhof, Saint-Petersburg, Russian Federation
Anna Petrovna Gorbenko

Saint -Petersburg State University, Faculty of Physics, 198504, Stary Peterhof, Saint-Petersburg, Russian Federation
Martin Tchoffo

Department of Physics, Faculty of Science, University of Dschang, Po Dschang, Cameroon

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Plain Text BibTeX RIS

APA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Martin Tchoffo. (2013). Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. American Journal of Modern Physics, 2(6), 334-340. https://doi.org/10.11648/j.ajmp.20130206.20

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ACS Style

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Martin Tchoffo. Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. Am. J. Mod. Phys. 2013, 2(6), 334-340. doi: 10.11648/j.ajmp.20130206.20

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AMA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Martin Tchoffo. Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells. Am J Mod Phys. 2013;2(6):334-340. doi: 10.11648/j.ajmp.20130206.20

Copy | Download

@article{10.11648/j.ajmp.20130206.20,
  author = {Galina Pavlovna Anisimova and Olga Aleksandrovna Dolmatova and Anna Petrovna Gorbenko and Martin Tchoffo},
  title = {Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells},
  journal = {American Journal of Modern Physics},
  volume = {2},
  number = {6},
  pages = {334-340},
  doi = {10.11648/j.ajmp.20130206.20},
  url = {https://doi.org/10.11648/j.ajmp.20130206.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130206.20},
  abstract = {In the energy operator matrix of four-level configurations with s and i -electrons in external shells, we take into account the following magnetic interactions: spin-other-orbit, spin-spin, and orbit-orbit interactions. The calculation of matrix elements is done in the uncoupled moments representation with subsequent translation (passage) to the LSJM- representation. Comparison with independent calculations in LSJM-representation for and configurations is done. The method of calculation in electronic configuration is extended to the holes configurations i^25 s As results the energy operator matrix is complemented with new physical conditions on radial integrals of Marvin’s spin interactions, which permits to ameliorate the precision of future calculations of fine structure parameters by semi-empirical methods.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Magnetic Interactions in the Energy Operator Matrix of Configurations with s and i Electrons in External Shells
AU  - Galina Pavlovna Anisimova
AU  - Olga Aleksandrovna Dolmatova
AU  - Anna Petrovna Gorbenko
AU  - Martin Tchoffo
Y1  - 2013/11/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130206.20
DO  - 10.11648/j.ajmp.20130206.20
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 334
EP  - 340
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20130206.20
AB  - In the energy operator matrix of four-level configurations with s and i -electrons in external shells, we take into account the following magnetic interactions: spin-other-orbit, spin-spin, and orbit-orbit interactions. The calculation of matrix elements is done in the uncoupled moments representation with subsequent translation (passage) to the LSJM- representation. Comparison with independent calculations in LSJM-representation for and configurations is done. The method of calculation in electronic configuration is extended to the holes configurations i^25 s As results the energy operator matrix is complemented with new physical conditions on radial integrals of Marvin’s spin interactions, which permits to ameliorate the precision of future calculations of fine structure parameters by semi-empirical methods.
VL  - 2
IS  - 6
ER  -

Copy | Download