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

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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[2] Lindroth E 1994. Calculation of doubly excited states of helium with a finite discrete spectrum. Phys. Rev. A 49, 4473.
[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.
[5] Ivanov A I and Safronova I U 1993. Calculation of the correlation part of the energy of two-electron systems. Opt. Spectrosk 75, 516.
[6] Roy K A, Singh R and Deb M B 1997. Density-functional calculations for doubly excited states of He, Li+, Be2+ and B3+ (1,3Se, 3P°, 1,3De, 1,3P, 1Ge). J. Phys. B: At. Mol. Opt. Phys. 30, 4763.
[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 1Se, 1De and 1Ge 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) 1Se, (np2) 1De 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 1,3Se, 1,3P° and 1,3De 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.
[19] Drake G W 1988 Theoretical energies for the n = 1 and 2 states of the helium isoelectronic sequence up to Z = 100 Can. J. Phys. 66 586.
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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
  • Department of Physics, UFR Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal

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

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

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

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

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

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