| Peer-Reviewed

The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions

Received: 16 January 2020     Accepted: 6 February 2020     Published: 10 March 2020
Views:       Downloads:
Abstract

In this paper, we have applied the complex rotation method to the calculations energies of the ground state (1s22s) 2S and the low-lying excited (1s2ns)2S states with n = 3, 4 and 5; of lithium and its isoelectronic series. For the ground state, the calculations were made up to Z = 20 and for the low-lying excited states up to Z = 10. These energies calculations were made using new special forms of Hylleraas-type wave functions designed by combining incomplete radial hydrogenic wave functions and Hylleraas-type wave functions. Using a numerical calculation program, the values of the resonance energies are calculated. Our results are compared with the results of ab-initio calculations using Hylleraas type wave functions and with semi-empirical results by Screening Constant by Unit Nuclear Charge (SCUNC) formalism. Analysis of the present results is achieved by calculating the ratio and the difference between our values and those of other authors. The results obtained are in good agreement with those of the theoretical methods available in the literature. This agreement shows the adequacy of our wave function with small bases to satisfactorily describe the ground state and the low-lying excited states of the three-electron atomic systems.

Published in International Journal of High Energy Physics (Volume 7, Issue 1)
DOI 10.11648/j.ijhep.20200701.11
Page(s) 1-7
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), 2020. Published by Science Publishing Group

Keywords

Wave Function, Resonance Parameters, Correlation Factors, Resonant Width, Ground State, Low-lying Excited States, Li-like Ions

References
[1] R. P. Madden and K. Codling, Astrophys. J. 141, 364, (1965).
[2] P. Dhez and D. L. Ederer, J. Phys. B 6, L59 (1973).
[3] P. K. Carroll and E. T. Kennedy, Phys. Rev. Lett. 38, 1068, (1977).
[4] H. D. Morgan and D. L. Ederer, Phys. Rev. A., 29, 1901, (1984).
[5] P. R. Woodruff and J. A. R. Samson, Phys. Rev. A., 25, 848, (1982).
[6] G. Herzberg and H. R. Moore, Can. J. Phys., 37, 1293, (1959).
[7] H. G. Berry, Phy. Scr., 12, 5–20, (1975).
[8] C. Eckart, Phys. Rev., 36, 878, (1930).
[9] V. Guillemin Jr., and C. Zener, Z. Phys., 61, 199, (1930).
[10] E. B. Wilson Jr., J. Chem. Phys., 1, 210, (1933).
[11] H. M. James, and A. S. Coolidge, Phys. Rev., 47, 700, (1935).
[12] H. M. James, and A. S. Coolidge, Phys. Rev., 49, 688, (1936).
[13] A. W. Weiss, Phys. Rev., 122, 1826, (1961).
[14] S. Larsson, Phys. Rev., 169, 49 (1968).
[15] J. Muszynska, D. Papierowska, and W. Woznicki, Chem. Phys. Lett., 76, 136, (1980).
[16] F. W. King, and V. Shoup, Phys. Rev. A., 33, 2940, (1986).
[17] F. W. King, Phys. Rev. A., 40, 1735, (1989).
[18] F. W. King, and M. P. Bergsbaken, J. Chem. Phys., 93, 2570, (1990).
[19] D. K. McKenzie, and G. W. F. Drake, Phys. Rev. A., 44, R6973, (1991).
[20] A. Luchow, and H. Kleindienst, Int. J. Quantum Chem., 51, 211, (1994).
[21] Z. C. Yan, and G. W. F. Drake, Phys. Rev. A., 52, 3711, (1995).
[22] Z. C. Yan, M. Tambasco, and G. W. F. Drake, Phys. Rev. A., 57, 1652, (1998).
[23] Z. W. Wang, X. W. Zhu, and K. T. Chung, Phys. Rev. A., 46, 6914 (1992).
[24] Z. W. Wang, X. W. Zhu, and K. T. Chung, Phys. Scr., 47, 65 (1993).
[25] Y. K. Ho, Intern. J. of Quant. Chem., 10, pp. 1077-1082, (1981).
[26] Y. K. Ho, Physics Reports 99, N°1, 1 – 68, (1983).
[27] Y. K. Ho, J. Phys. B, 12, p. 387 (1979).
[28] M. Biaye, M. Dieng, I. Sakho, and A. Wagué, Chin. J. Phys., 47, 166 (2009).
[29] M. Biaye, A. Konté, N. A. B. Faye, and A. Wagué, Eur. Phys. J. D, 13, 21 (2001).
[30] M. Biaye, A. Konte, A. S. Ndao, N. A. B. Faye, and A. Wague, Phys. Scr., 71, 39-42 (2005).
[31] M. Biaye, A. Konté, A. S. Ndao, and A. Wague, Phys. Scr., 72, 373 (2005).
[32] M. Biaye, Thèse de Doctorat d’Etat, Université Cheikh Anta Diop de Dakar (2005).
[33] M. Dieng, I. Sakho, M. Biaye, and A. Wague, Chin. J. Phys., 48, 1 (2010).
[34] M. Dieng, M. Biaye, Y. Gning, and A. Wague, Chin. J. Phys., 51, 4 (2013).
[35] Y. Gning, M. Sow, A. Traoré, M. Dieng, B. Diakhate, M. Biaye, and A. Wague, Rad. Phys. Chem., 106, 1, (2015).
[36] Y. Gning, Thèse de Doctorat, Université Cheikh Anta Diop de Dakar, (2016).
[37] D. A. Varshalovich al., (Copyright by Scientific Publishing copte ltd 1988).
[38] C. Bunge, Phys. Rev. A., 16, 249, (1977).
[39] A. J. Thakkar, T. Koga, T. Tanabe, and H. Teruya, Chem. Phys. Lett., 366, p. 95–99, (2002).
[40] I. Sakho, and A. Wague, Chin. J. Phys., 48, 5, (2010).
[41] K. T. Chung, Phys. Rev. A., 44, 9, (1991).
[42] K. T. Chung, Phys. Rev. A., 45, 11, (1992).
[43] K. T. Chung, and X. W. Zhu, Physica Scripta., 48, 292-296, (1993).
[44] I. Sakho, Chin. J. Phys., 52, 5, (2014).
[45] F. W. King, Phys. Rev. A., 43, 7, (1991).
Cite This Article
  • APA Style

    Babou Diop, Youssou Gning, Maurice Faye, Abdou Diouf, Boubacar Sow, et al. (2020). The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions. International Journal of High Energy Physics, 7(1), 1-7. https://doi.org/10.11648/j.ijhep.20200701.11

    Copy | Download

    ACS Style

    Babou Diop; Youssou Gning; Maurice Faye; Abdou Diouf; Boubacar Sow, et al. The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions. Int. J. High Energy Phys. 2020, 7(1), 1-7. doi: 10.11648/j.ijhep.20200701.11

    Copy | Download

    AMA Style

    Babou Diop, Youssou Gning, Maurice Faye, Abdou Diouf, Boubacar Sow, et al. The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions. Int J High Energy Phys. 2020;7(1):1-7. doi: 10.11648/j.ijhep.20200701.11

    Copy | Download

  • @article{10.11648/j.ijhep.20200701.11,
      author = {Babou Diop and Youssou Gning and Maurice Faye and Abdou Diouf and Boubacar Sow and Malick Sow and Matabara Dieng and Mamadi Biaye},
      title = {The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions},
      journal = {International Journal of High Energy Physics},
      volume = {7},
      number = {1},
      pages = {1-7},
      doi = {10.11648/j.ijhep.20200701.11},
      url = {https://doi.org/10.11648/j.ijhep.20200701.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20200701.11},
      abstract = {In this paper, we have applied the complex rotation method to the calculations energies of the ground state (1s22s) 2S and the low-lying excited (1s2ns)2S states with n = 3, 4 and 5; of lithium and its isoelectronic series. For the ground state, the calculations were made up to Z = 20 and for the low-lying excited states up to Z = 10. These energies calculations were made using new special forms of Hylleraas-type wave functions designed by combining incomplete radial hydrogenic wave functions and Hylleraas-type wave functions. Using a numerical calculation program, the values of the resonance energies are calculated. Our results are compared with the results of ab-initio calculations using Hylleraas type wave functions and with semi-empirical results by Screening Constant by Unit Nuclear Charge (SCUNC) formalism. Analysis of the present results is achieved by calculating the ratio and the difference between our values and those of other authors. The results obtained are in good agreement with those of the theoretical methods available in the literature. This agreement shows the adequacy of our wave function with small bases to satisfactorily describe the ground state and the low-lying excited states of the three-electron atomic systems.},
     year = {2020}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - The Ground State (1s22s)2S and the Low-lying Excited (1s2ns)2S States Energy Calculations of Li-Like Ions Using Special Forms of the Hylleraas-Type Wave Functions
    AU  - Babou Diop
    AU  - Youssou Gning
    AU  - Maurice Faye
    AU  - Abdou Diouf
    AU  - Boubacar Sow
    AU  - Malick Sow
    AU  - Matabara Dieng
    AU  - Mamadi Biaye
    Y1  - 2020/03/10
    PY  - 2020
    N1  - https://doi.org/10.11648/j.ijhep.20200701.11
    DO  - 10.11648/j.ijhep.20200701.11
    T2  - International Journal of High Energy Physics
    JF  - International Journal of High Energy Physics
    JO  - International Journal of High Energy Physics
    SP  - 1
    EP  - 7
    PB  - Science Publishing Group
    SN  - 2376-7448
    UR  - https://doi.org/10.11648/j.ijhep.20200701.11
    AB  - In this paper, we have applied the complex rotation method to the calculations energies of the ground state (1s22s) 2S and the low-lying excited (1s2ns)2S states with n = 3, 4 and 5; of lithium and its isoelectronic series. For the ground state, the calculations were made up to Z = 20 and for the low-lying excited states up to Z = 10. These energies calculations were made using new special forms of Hylleraas-type wave functions designed by combining incomplete radial hydrogenic wave functions and Hylleraas-type wave functions. Using a numerical calculation program, the values of the resonance energies are calculated. Our results are compared with the results of ab-initio calculations using Hylleraas type wave functions and with semi-empirical results by Screening Constant by Unit Nuclear Charge (SCUNC) formalism. Analysis of the present results is achieved by calculating the ratio and the difference between our values and those of other authors. The results obtained are in good agreement with those of the theoretical methods available in the literature. This agreement shows the adequacy of our wave function with small bases to satisfactorily describe the ground state and the low-lying excited states of the three-electron atomic systems.
    VL  - 7
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Atoms Laser Laboratory, Department of physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop, Dakar, Senegal

  • Atoms Laser Laboratory, Department of physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop, Dakar, Senegal

  • Department of Experiential Sciences, UFR Sciences and Technologies, University of Thies, Thies, Senegal

  • Atoms Laser Laboratory, Department of physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop, Dakar, Senegal

  • Atoms Laser Laboratory, Department of physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop, Dakar, Senegal

  • Atoms Laser Laboratory, Department of physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop, Dakar, Senegal

  • Department of Physics, UFR Applied Sciences and Technologies of Information and Communication, University Alioune DIOP of Bambey, Bambey, Senegal

  • Departments of Physics and Chemistry, Faculty of Sciences and Technologies of Formation and Education, University Cheikh Anta Diop, Dakar, Senegal

  • Sections