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

Babou Diop; Youssou Gning; Maurice Faye; Abdou Diouf; Boubacar Sow; Malick Sow; Matabara Dieng; Mamadi Biaye

doi:doi:10.11648/j.ijhep.20200701.11

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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

Babou Diop, Youssou Gning, Maurice Faye, Abdou Diouf, Boubacar Sow, Malick Sow, Matabara Dieng, Mamadi Biaye

Published in International Journal of High Energy Physics (Volume 7, Issue 1)

Received: 16 January 2020 Accepted: 6 February 2020 Published: 10 March 2020

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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

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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

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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

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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

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@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}
}

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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  -

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Author Information

Babou Diop

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

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

Department of Experiential Sciences, UFR Sciences and Technologies, University of Thies, Thies, Senegal
Abdou Diouf

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

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

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

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

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

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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

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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

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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  -

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