Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism

Jean Kouhissoré Badiane; Mamadou Diouldé Ba; Abdourahmane Diallo; Momar Talla Nging; Malick Sow; Ibrahima Sakho

doi:doi:10.11648/j.ijamtp.20180402.11

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Variationnal Calculation of the Doubly (nl) ² ¹L^p Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism

Jean Kouhissoré Badiane, Mamadou Diouldé Ba, Abdourahmane Diallo, Momar Talla Nging, Malick Sow, Ibrahima Sakho

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 2)

Received: 19 May 2018 Accepted: 20 June 2018 Published: 16 July 2018

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Abstract

The present work deals with an ab initio calculation of total energies of the doubly excited np², nd² and nf² states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np², nd² and nf² excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 2)
DOI	10.11648/j.ijamtp.20180402.11
Page(s)	27-41
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

Ab Initio Calculation, Doubly Excited, Total Energy, Helium-Like Systems, Correlated Wave Function, Screening Constant by Unit Nuclear Charge

References

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[3]	Ho Y K and Callaway J 1985. Doubly excited states of helium atoms between the N = 2 and N = 3 He⁺ thresholds. J. Phys. B: At. Mol. Phys. 18, 3481.
[4]	Biaye M, Konte A, Faye B A N and Wague A 2005. The Singlet Doubly Excited (nl) ² States of Helium-Like Systems. Phys. Scr. 71, 39.
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[7]	Bachau H, Martin F, Riera A and Yanez M 1991. Helium-like doubly excited states At. Data Nucl. Data Tables 48, 167.
[8]	Ho Y K 1989. Resonances in helium atoms associated with the N = 4 and N = 5 He⁺ thresholds Z. Phys. D 11, 277.
[9]	Macias A, Martin F, Riera A and Yanez M 1987. Simple discretization method for autoionization widths. II. Atoms Phys. Rev. A 36, 4187.
[10]	Conneely M J and Lipsky L 1978. Widths and configuration mixings of two-electron systems below the N = 2 threshold. J. Phys. B: At. Mol. Phys. 24, 4135.
[11]	Ray D and Mukherjee P K 1991. Doubly excited ¹S^e, ¹D^e and ¹G^e states of He, Li⁺, Be²⁺ and B³⁺. J. Phys. B: At. Mol. Opt. Phys. 24, 1241.
[12]	Sakho I, Ndao A S, Biaye M and Wague 2008. Screening Constant by Unit Nuclear Charge calculations for (ns²) ¹S^e, (np²) ¹D^e and (Nsnp) ¹P° excited states of He – like systems. Eur. Phys. J. D 47, 37.
[13]	Sakho I, Ndao A S, Biaye M and Wague 2010. Calculations of (nl) ² and (3lnl’) autoionizing states in two electron systems. Phys. Scr. 82, 035301.
[14]	Sakho I, Ndao A S, Biaye M and Wague 2008. Investigation of 2snp ± 1, 3 P° resonances of two-electron systems using Screening Constant by Unit Nuclear Charge method. Phys. Scr.77, 055303.
[15]	Sakho I 2010. High-lying ¹P° doubly-excited states of H- and He below the N = 3 -13 hydrogenic thresholds. Eur. Phys. J. D 59, 171.
[16]	Sakho I 2011. Screening Constant by Unit Nuclear Charge calculations of ^1,3S^e, ^1,3P° and ^1,3D^e Intershell Rydberg states of the helium – like ions below the N = 2 hydrogenic threshold. Eur. Phys. J. D 61, 267.
[17]	Sakho I 2017. Energies of doubly excited 1,3P° resonances in He-like (Z = 2 – 40) systems below the N = 3 hydrogenic threshold. At. Data Nucl. Data Tables 117, 425.
[18]	Sakho I, Ndao A S, Biaye M and Wague 2006 Calculation of the ground-state energy, the first ionization energy and the radial correlation expectation value for He-like atoms. Phys. Scr. 74, 180.
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APA Style

Jean Kouhissoré Badiane, Mamadou Diouldé Ba, Abdourahmane Diallo, Momar Talla Nging, Malick Sow, et al. (2018). Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. International Journal of Applied Mathematics and Theoretical Physics, 4(2), 27-41. https://doi.org/10.11648/j.ijamtp.20180402.11

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ACS Style

Jean Kouhissoré Badiane; Mamadou Diouldé Ba; Abdourahmane Diallo; Momar Talla Nging; Malick Sow, et al. Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. Int. J. Appl. Math. Theor. Phys. 2018, 4(2), 27-41. doi: 10.11648/j.ijamtp.20180402.11

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AMA Style

Jean Kouhissoré Badiane, Mamadou Diouldé Ba, Abdourahmane Diallo, Momar Talla Nging, Malick Sow, et al. Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. Int J Appl Math Theor Phys. 2018;4(2):27-41. doi: 10.11648/j.ijamtp.20180402.11

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@article{10.11648/j.ijamtp.20180402.11,
  author = {Jean Kouhissoré Badiane and Mamadou Diouldé Ba and Abdourahmane Diallo and Momar Talla Nging and Malick Sow and Ibrahima Sakho},
  title = {Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {2},
  pages = {27-41},
  doi = {10.11648/j.ijamtp.20180402.11},
  url = {https://doi.org/10.11648/j.ijamtp.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180402.11},
  abstract = {The present work deals with an ab initio calculation of total energies of the doubly excited np2, nd2 and nf2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np2, nd2 and nf2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.},
 year = {2018}
}

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TY  - JOUR
T1  - Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism
AU  - Jean Kouhissoré Badiane
AU  - Mamadou Diouldé Ba
AU  - Abdourahmane Diallo
AU  - Momar Talla Nging
AU  - Malick Sow
AU  - Ibrahima Sakho
Y1  - 2018/07/16
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180402.11
DO  - 10.11648/j.ijamtp.20180402.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 27
EP  - 41
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180402.11
AB  - The present work deals with an ab initio calculation of total energies of the doubly excited np2, nd2 and nf2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np2, nd2 and nf2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.
VL  - 4
IS  - 2
ER  -

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Author Information

Jean Kouhissoré Badiane

Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal
Mamadou Diouldé Ba

Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal
Abdourahmane Diallo

Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal
Momar Talla Nging

Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal
Malick Sow

Department of Physics, Faculty of Sciences and Techniques, University Cheikh Anta Diop of Dakar, Dakar, Senegal
Ibrahima Sakho

Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal

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Plain Text BibTeX RIS

APA Style

Jean Kouhissoré Badiane, Mamadou Diouldé Ba, Abdourahmane Diallo, Momar Talla Nging, Malick Sow, et al. (2018). Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. International Journal of Applied Mathematics and Theoretical Physics, 4(2), 27-41. https://doi.org/10.11648/j.ijamtp.20180402.11

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ACS Style

Jean Kouhissoré Badiane; Mamadou Diouldé Ba; Abdourahmane Diallo; Momar Talla Nging; Malick Sow, et al. Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. Int. J. Appl. Math. Theor. Phys. 2018, 4(2), 27-41. doi: 10.11648/j.ijamtp.20180402.11

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AMA Style

Jean Kouhissoré Badiane, Mamadou Diouldé Ba, Abdourahmane Diallo, Momar Talla Nging, Malick Sow, et al. Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism. Int J Appl Math Theor Phys. 2018;4(2):27-41. doi: 10.11648/j.ijamtp.20180402.11

Copy | Download

@article{10.11648/j.ijamtp.20180402.11,
  author = {Jean Kouhissoré Badiane and Mamadou Diouldé Ba and Abdourahmane Diallo and Momar Talla Nging and Malick Sow and Ibrahima Sakho},
  title = {Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {2},
  pages = {27-41},
  doi = {10.11648/j.ijamtp.20180402.11},
  url = {https://doi.org/10.11648/j.ijamtp.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180402.11},
  abstract = {The present work deals with an ab initio calculation of total energies of the doubly excited np2, nd2 and nf2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np2, nd2 and nf2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Variationnal Calculation of the Doubly (nl) 2 1Lp Excited States of He-Like Ions Via the Screening Constant by Unit Nuclear Charge Formalism
AU  - Jean Kouhissoré Badiane
AU  - Mamadou Diouldé Ba
AU  - Abdourahmane Diallo
AU  - Momar Talla Nging
AU  - Malick Sow
AU  - Ibrahima Sakho
Y1  - 2018/07/16
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180402.11
DO  - 10.11648/j.ijamtp.20180402.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 27
EP  - 41
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180402.11
AB  - The present work deals with an ab initio calculation of total energies of the doubly excited np2, nd2 and nf2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np2, nd2 and nf2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.
VL  - 4
IS  - 2
ER  -

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