American Journal of Modern Physics

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First Order Expectation Values of Electron Correlation Operators for Two-Electron Atoms

Received: 8 January 2015    Accepted: 28 January 2015    Published: 6 March 2015
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Abstract

Simple analytic first-order wave functions corresponding to two-electron atoms electron correlation operators are obtained by reduction of the Rayleigh-Schrödinger first order perturbation equation to that of one-electron through the partial integration over the variables of one electron. The resulting first order wave functions are applied to evaluate the first order expectation values of electron correlation operators associated with the radial correlation, magnetic shielding and diamagnetic susceptibility. The results obtained have close agreement with other theoretical results.

DOI 10.11648/j.ajmp.20150402.14
Published in American Journal of Modern Physics (Volume 4, Issue 2, March 2015)
Page(s) 70-74
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

First Order Wave Functions, Radial Correlation, Magnetic Shielding and Diamagnetic Susceptibility

References
[1] Bethe H A and Salpeter E E. (1957). Quantum mechanics of one- and two-electron Atoms. Berlin: Springer-Verlag.
[2] Coundon E U and Shortely G H. (1959). The theory of atomic spectra. London: Camdridge University Press.
[3] Greiner, W. (2000). Quantum Mechanics. Berlin: Springer Verlag.
[4] Dalgarno A and Stewart A L. (1958). A perturbation calculation for properties of helium iso-electronic sequence. Proc. Roy. Soc.( London), A 247 , 245-249.
[5] Dalgarno A and Stewart A L. (1960). The screening approximation for the Helium Sequence. Proc. Roy. Soc. A , 534-540.
[6] Hall G G, Jones L L and Rees D. (1965). The first-order density matrix for the direct calculation of atoms. Proc. Roy. Soc. A , 194-202
[7] Utpal R and Talekdar B. (1999). Electron correction for Helium-like stoms. Physica Scripta, Vol 59 , 133-137.
[8] Sakho I. Ndao A S, Biaye M and Wague A. (2006). Calculation of the groung state energy, the first ionization energy and radial correlation expectation value for He-like atoms. Phy, Scr. 74 , 180-18
[9] Sakho I, Ndao A S, Biaye M and Wague A. (2008). Screening constant by unit nuclear charge for (ns)S, (np)D and (nsnp) P excited states of He-like system. Eur. Phys. J. D 47 , 37-44.
[10] Ndinya B O and Omolo J A. (2010). A direct calculation of first order wave function of Helium. Commun. Thor. Physics. 54 , 647-650.
[11] Omolo J A and Ndinya B O. (2009). Repulsive Coulomb interaction and nuclear charge screening in Helium and Helium-like ions. Indian. J. Theor. Phys. 58 , 81-85.
[12] Merzbacher, E. (1970). Quantum Mechanics. New York: John Wiley and son.
[13] Pekeris, C. (1958). Ground state of two electron atoms. Phys. Rev. 112 , 1649.
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    Boniface Otieno Ndinya, Florence Mutonyi D’ujanga, Jacob Olawo Oduogo, Andrew Odhiambo Oduor, Joseph Omolo Akeyo. (2015). First Order Expectation Values of Electron Correlation Operators for Two-Electron Atoms. American Journal of Modern Physics, 4(2), 70-74. https://doi.org/10.11648/j.ajmp.20150402.14

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    ACS Style

    Boniface Otieno Ndinya; Florence Mutonyi D’ujanga; Jacob Olawo Oduogo; Andrew Odhiambo Oduor; Joseph Omolo Akeyo. First Order Expectation Values of Electron Correlation Operators for Two-Electron Atoms. Am. J. Mod. Phys. 2015, 4(2), 70-74. doi: 10.11648/j.ajmp.20150402.14

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    AMA Style

    Boniface Otieno Ndinya, Florence Mutonyi D’ujanga, Jacob Olawo Oduogo, Andrew Odhiambo Oduor, Joseph Omolo Akeyo. First Order Expectation Values of Electron Correlation Operators for Two-Electron Atoms. Am J Mod Phys. 2015;4(2):70-74. doi: 10.11648/j.ajmp.20150402.14

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  • @article{10.11648/j.ajmp.20150402.14,
      author = {Boniface Otieno Ndinya and Florence Mutonyi D’ujanga and Jacob Olawo Oduogo and Andrew Odhiambo Oduor and Joseph Omolo Akeyo},
      title = {First Order Expectation Values of Electron Correlation Operators for Two-Electron Atoms},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {2},
      pages = {70-74},
      doi = {10.11648/j.ajmp.20150402.14},
      url = {https://doi.org/10.11648/j.ajmp.20150402.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150402.14},
      abstract = {Simple analytic first-order wave functions corresponding to two-electron atoms electron correlation operators are obtained by reduction of the Rayleigh-Schrödinger first order perturbation equation to that of one-electron through the partial integration over the variables of one electron. The resulting first order wave functions are applied to evaluate the first order expectation values of electron correlation operators associated with the radial correlation, magnetic shielding and diamagnetic susceptibility. The results obtained have close agreement with other theoretical results.},
     year = {2015}
    }
    

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    AB  - Simple analytic first-order wave functions corresponding to two-electron atoms electron correlation operators are obtained by reduction of the Rayleigh-Schrödinger first order perturbation equation to that of one-electron through the partial integration over the variables of one electron. The resulting first order wave functions are applied to evaluate the first order expectation values of electron correlation operators associated with the radial correlation, magnetic shielding and diamagnetic susceptibility. The results obtained have close agreement with other theoretical results.
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Author Information
  • Department of Physics and Material Science, Maseno University, Maseno, Kenya; Department of Physics, Makerere University, Kampala, Uganda

  • Department of Physics, Makerere University, Kampala, Uganda

  • Department of Physics, Masinde Muliro University of Science and Technology, Kakamega, Kenya

  • Department of Physics and Material Science, Maseno University, Maseno, Kenya

  • Department of Physics and Material Science, Maseno University, Maseno, Kenya

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