Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Igor Ratmirovich Krylov; Igor Cheslavovich Mashek; Martin Tchoffo; Galina Aleksandrovna Tsygankova

doi:doi:10.11648/j.ajmp.20150406.17

Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Igor Ratmirovich Krylov, Igor Cheslavovich Mashek, Martin Tchoffo, Galina Aleksandrovna Tsygankova

Published in American Journal of Modern Physics (Volume 4, Issue 6)

Received: 14 December 2015 Accepted: 21 December 2015 Published: 4 January 2016

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Abstract

The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios — one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.

Published in	American Journal of Modern Physics (Volume 4, Issue 6)
DOI	10.11648/j.ajmp.20150406.17
Page(s)	296-303
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), 2016. Published by Science Publishing Group

Keywords

Fine Structure, Zeeman Splitting, Crossings and Anticrossings of Magnetic Components, Gyromagnetic Ratios, Energy Operator Matrix

References

[1]	L. Johansson, Spectrum and term system of the neutral carbon atom, Arkiv för Physik 31 (15), 201 (1966).
[2]	Edward S. Chang, and Murray Geller, Improved Experimental Energy Levels of Carbon I from Solar Infrared Spectra, Phys. Scr. 58, 330 (1998).
[3]	L. J. Radziemski, K. L. Andrew, V. Kaufman, and U. Litzen, Vacuum Ultraviolet Wavelength Standards and Improved Energy Levels in the Fist Spectrum of Silicon, J. Opt. Soc. Am. 57 (3), 336 (1967).
[4]	G. P. Anisimova, and E. L. Kapel`kina, Spin-Other-Orbit Interaction in Two-Electron Configurations with p and f Electrons: Direct Terms, Optics and Spectroscopy 84 (3), 313 (1998).
[5]	G. P. Anisimova, and E. L. Kapel`kina, Spin-Other-Orbit Interaction in Two-Electron Configurations with p and f Electrons: Excharge Terms, Optics and Spectroscopy 84 (4), 476 (1998).
[6]	G. P. Anisimova, and E. L. Kapel`kina, Two-Electron Matrices of the Total Energy Operator of the Spin-Orbit Magnetic Interaction for pf, p⁵f, fp, and f¹³p Configurations, Optics and Spectroscopy 84 (6), 799 (1998).
[7]	G. P. Anisimova, and E. L. Kapel`kina, Account for the Spin-Spin Interaction in the Energy Matrices of Two-Electron Configurations with p and f Electrons, Optics and Spectroscopy 87 (1), 9 (1999).
[8]	G. P. Anisimova, and E. L. Kapel`kina, Orbit-Orbit Interaction in Two-Electron Matrices of the Energy Operator for pf Configurations, Optics and Spectroscopy 87 (6), 805 (1999).
[9]	G. P. Anisimova, O. A. Dolmatova, M. Choffo, Determination of Gyromagnetic Ratios from the Zeeman Splitting of Levels of the 3p5f Configuration of the Silicon Atom, Optics and Spectroscopy 114 (2), 177 (2013).
[10]	G. P. Anisimova, I. Ch. Mashek, O. A. Dolmatova, A. P. Gorbenko, R. I. Semenov, and M. L. Tchoffo, Features of the Zeeman splitting and g-factors of 2p5f configuration levels of carbon atom, American Journal of Modern Physics 3 (6), 218 (2014).
[11]	NIST Atomic Spectra Database Levels Data. C I 282 Levels Found. 2009.
[12]	NIST Atomic Spectra Database Levels Data. Si I 542 Levels Found. 2008.
[13]	A. P. Yutsis, and A. Yu. Savukinas, Mathematical Foundations of the Theory of Atom (Vil`nyus, 1973) [in Russian].
[14]	D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of the Angular Moment, Leningrad, 1975 [in Russian].
[15]	I. I. Sobelman, Introduction to the Theory of Atomic Spectras (Moscow, 1963) [in Russian].
[16]	G. P. Anisimova, O. A. Dolmatova, and I. S. Rusnak, Spin–Other Orbit Interaction in Highly Exited Configurations with p and g Electrons in Outer Shells, Optics and Spectroscopy 107 (4), 545 (2009).
[17]	G. P. Anisimova, I. Ch. Mashek, O. A. Dolmatova, A. P. Gorbenko, R. I. Semenov, M. Tchoffo, G. A. Tsygankova, 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 (2014).
[18]	J. B. Green, and J. F. Eichelberger, The Pashen-Back Effect. Theory of the Effect for Intermediate Coupling, Phys. Rev. 56 (1), 51 (1939).
[19]	V. Kaufman, and J. Sugar, Wavelengths and Energy Level Classifications of Scandium Spectra for All stages of Ionization, J. Phys. Chem. Ref. Data 17 (4), 1679 (1988).

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Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Igor Ratmirovich Krylov, Igor Cheslavovich Mashek, et al. (2016). Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. American Journal of Modern Physics, 4(6), 296-303. https://doi.org/10.11648/j.ajmp.20150406.17

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ACS Style

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Igor Ratmirovich Krylov; Igor Cheslavovich Mashek, et al. Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. Am. J. Mod. Phys. 2016, 4(6), 296-303. doi: 10.11648/j.ajmp.20150406.17

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AMA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Igor Ratmirovich Krylov, Igor Cheslavovich Mashek, et al. Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. Am J Mod Phys. 2016;4(6):296-303. doi: 10.11648/j.ajmp.20150406.17

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@article{10.11648/j.ajmp.20150406.17,
  author = {Galina Pavlovna Anisimova and Olga Aleksandrovna Dolmatova and Anna Petrovna Gorbenko and Igor Ratmirovich Krylov and Igor Cheslavovich Mashek and Martin Tchoffo and Galina Aleksandrovna Tsygankova},
  title = {Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms},
  journal = {American Journal of Modern Physics},
  volume = {4},
  number = {6},
  pages = {296-303},
  doi = {10.11648/j.ajmp.20150406.17},
  url = {https://doi.org/10.11648/j.ajmp.20150406.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150406.17},
  abstract = {The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios — one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.},
 year = {2016}
}

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TY  - JOUR
T1  - Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms
AU  - Galina Pavlovna Anisimova
AU  - Olga Aleksandrovna Dolmatova
AU  - Anna Petrovna Gorbenko
AU  - Igor Ratmirovich Krylov
AU  - Igor Cheslavovich Mashek
AU  - Martin Tchoffo
AU  - Galina Aleksandrovna Tsygankova
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20150406.17
DO  - 10.11648/j.ajmp.20150406.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 296
EP  - 303
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20150406.17
AB  - The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios — one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.
VL  - 4
IS  - 6
ER  -

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Author Information

Galina Pavlovna Anisimova

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia
Olga Aleksandrovna Dolmatova

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia
Anna Petrovna Gorbenko

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia
Igor Ratmirovich Krylov

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia
Igor Cheslavovich Mashek

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia
Martin Tchoffo

Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, Dschang, Cameroon
Galina Aleksandrovna Tsygankova

Physics Department, Saint-Petersburg State University, Saint-Petersburg, Russia

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APA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Igor Ratmirovich Krylov, Igor Cheslavovich Mashek, et al. (2016). Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. American Journal of Modern Physics, 4(6), 296-303. https://doi.org/10.11648/j.ajmp.20150406.17

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ACS Style

Galina Pavlovna Anisimova; Olga Aleksandrovna Dolmatova; Anna Petrovna Gorbenko; Igor Ratmirovich Krylov; Igor Cheslavovich Mashek, et al. Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. Am. J. Mod. Phys. 2016, 4(6), 296-303. doi: 10.11648/j.ajmp.20150406.17

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AMA Style

Galina Pavlovna Anisimova, Olga Aleksandrovna Dolmatova, Anna Petrovna Gorbenko, Igor Ratmirovich Krylov, Igor Cheslavovich Mashek, et al. Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms. Am J Mod Phys. 2016;4(6):296-303. doi: 10.11648/j.ajmp.20150406.17

Copy | Download

@article{10.11648/j.ajmp.20150406.17,
  author = {Galina Pavlovna Anisimova and Olga Aleksandrovna Dolmatova and Anna Petrovna Gorbenko and Igor Ratmirovich Krylov and Igor Cheslavovich Mashek and Martin Tchoffo and Galina Aleksandrovna Tsygankova},
  title = {Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms},
  journal = {American Journal of Modern Physics},
  volume = {4},
  number = {6},
  pages = {296-303},
  doi = {10.11648/j.ajmp.20150406.17},
  url = {https://doi.org/10.11648/j.ajmp.20150406.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150406.17},
  abstract = {The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios — one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms
AU  - Galina Pavlovna Anisimova
AU  - Olga Aleksandrovna Dolmatova
AU  - Anna Petrovna Gorbenko
AU  - Igor Ratmirovich Krylov
AU  - Igor Cheslavovich Mashek
AU  - Martin Tchoffo
AU  - Galina Aleksandrovna Tsygankova
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20150406.17
DO  - 10.11648/j.ajmp.20150406.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 296
EP  - 303
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20150406.17
AB  - The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios — one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.
VL  - 4
IS  - 6
ER  -

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