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Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms

Received: 22 February 2018     Accepted: 14 March 2018     Published: 8 April 2018
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Abstract

A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the context of perturbation theory. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number Z.

Published in Nuclear Science (Volume 3, Issue 1)
DOI 10.11648/j.ns.20180301.11
Page(s) 1-8
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), 2018. Published by Science Publishing Group

Keywords

Single-Electron Atoms, Relativistic Correction, First-Order Perturbation Theory, Nuclear Charge Number

References
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[2] P. Jonsson and C. F. Fischer, Comput. Phys. Commun. 100 (1997) 81.
[3] B. C. Tiburzi and B. R. Holstein, Am. J. Phys. 68 (2000) 640.
[4] K. Pachucki, D. Leibfried, M. Weitz, A. Huber, W. Konig and T. W. Hnsch, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 177.
[5] J. L. Friar, J. Martorell and D. W. L. Sprung, Phys. Rev. A. 56 (1997) 4579.
[6] A. Huber, Th. Udem, B. Gross, J. Rrichert, M. Kourogi, K. Pachucki, M. Weitz and T. W. Hnsch, Phys. Rev. Lett. 80 (1998) 468.
[7] K. Pachucki, M. Weitz and T. W. Hnsch, Phys. Rev. A. 49 (1996) 2255.
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[9] V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii "Relativistic Quantum Theory" (Pergamon Press, Oxford, 1982).
[10] W. R. Johnson and G. Soff, At. Data Nuc. Data Tables 33,405 (1985).
[11] S. M. Wong," Introductory to Nuclear Physics", Credicted Intrnational Advanced Series, 2000.
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Cite This Article
  • APA Style

    Babak Nadiri Niri, Arash Anjami. (2018). Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms. Nuclear Science, 3(1), 1-8. https://doi.org/10.11648/j.ns.20180301.11

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    ACS Style

    Babak Nadiri Niri; Arash Anjami. Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms. Nucl. Sci. 2018, 3(1), 1-8. doi: 10.11648/j.ns.20180301.11

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    AMA Style

    Babak Nadiri Niri, Arash Anjami. Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms. Nucl Sci. 2018;3(1):1-8. doi: 10.11648/j.ns.20180301.11

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  • @article{10.11648/j.ns.20180301.11,
      author = {Babak Nadiri Niri and Arash Anjami},
      title = {Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms},
      journal = {Nuclear Science},
      volume = {3},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.ns.20180301.11},
      url = {https://doi.org/10.11648/j.ns.20180301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20180301.11},
      abstract = {A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the context of perturbation theory. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number Z.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms
    AU  - Babak Nadiri Niri
    AU  - Arash Anjami
    Y1  - 2018/04/08
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ns.20180301.11
    DO  - 10.11648/j.ns.20180301.11
    T2  - Nuclear Science
    JF  - Nuclear Science
    JO  - Nuclear Science
    SP  - 1
    EP  - 8
    PB  - Science Publishing Group
    SN  - 2640-4346
    UR  - https://doi.org/10.11648/j.ns.20180301.11
    AB  - A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the context of perturbation theory. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number Z.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

  • Department of Physics Ardabil Branch, Islamic Azad University, Ardabil, Iran

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