Skip to main content
SpringerLink
Log in

Variational Monte Carlo calculations of lithium atom in strong magnetic field

  • Atoms, Molecules, Optics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The variational Monte Carlo method is applied to investigate the ground state and some excited states of the lithium atom and its ions up to Z = 10 in the presence of an external magnetic field regime with γ = 0–100 arb. units. The effect of increasing field strength on the ground state energy is studied and precise values for the crossover field strengths were obtained. Our calculations are based on using accurate forms of trial wave functions, which were put forward in calculating energies in the absence of magnetic field. Furthermore, the value of Y at which ground-state energy of the lithium atom approaches to zero was calculated. The obtained results are in good agreement with the most recent values and also with the exact values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Haberl, A. D. Schwope, V. Hambaryan, G. Hasinge, and C. Motch, Astron. Astrophys. L 19, 403 (2003).

    Google Scholar 

  2. V. Hambaryan, R. Neuhäuser, F. Haberl, M. M. Hohle, and A. D. Schwope, Astron. Astrophys. L 9, 497 (2009).

    Google Scholar 

  3. V. Hambaryan, V. Suleimanov, A. D. Schwope, R. Neuhäuser, K. Werner, and A. Y. Potekhin, Astron. Astrophys. A 74, 534 (2011).

    Google Scholar 

  4. W. Becker, Astrophys. Space Sci. Lib. 357 (2009).

    Google Scholar 

  5. B. Külebi, S. Jordan, F. Euchner, B. T. Gänsicke, and H. Hirsch, Astron. Astrophys. 506, 1341 (2009).

    Article  ADS  Google Scholar 

  6. S. O. Kepler, I. Pelisoli, S. Jordan, S. J. Kleinman, D. Koester, B. Külebi, V. Peçanha, B. G. Castanheira, A. Nitta, J. E. S. Costa, D. E. Winget, A. Kanaan, and L. Fraga, Mon. Not. R. Astron. Soc. 429, 2934 (2013).

    Article  ADS  Google Scholar 

  7. H. Ruder, G. Wunner, H. Herold, and F. Geyer, Atoms in Strong Magnetic Fields, Astron. Astrophys. Lib. (Springer, Berlin, 1994).

    Book  Google Scholar 

  8. L. B. Zhao and P. C. Stancil, J. Phys. B 40, 4347 (2007).

    Article  ADS  Google Scholar 

  9. Y. P. Kravchenko, M. A. Liberman, and B. Johansson, Phys. Rev. A 54, 287 (1996).

    Article  ADS  Google Scholar 

  10. Y. P. Kravchenko, M. A. Liberman, and B. Johansson, Phys. Rev. Lett. 77, 619 (1996).

    Article  ADS  Google Scholar 

  11. W. Rösner, G. Wunner, H. Herold, and H. Ruder, J. Phys. B: At. Mol. Opt. Phys. 17, 29 (1984).

    Article  ADS  Google Scholar 

  12. M. V. Ivanov, J. Phys. B, At. Mol. Opt. Phys. 21, 447 (1988).

    Article  ADS  Google Scholar 

  13. S. Jordan, P. Schmelcher, W. Becken, and W. Schweizer, Astron. Astrophys. L33–L36, 336 (1998).

    Google Scholar 

  14. R. J. Elliot and R. Loudon, J. Phys. Chem. Sol. 15, 196 (1960).

    Article  ADS  Google Scholar 

  15. M. V. Ivanov, Opt. Spectrosc. 70, 148 (1991).

    ADS  Google Scholar 

  16. M. V. Ivanov, J. Phys. B: At. Mol. Opt. Phys. 27, 4513 (1994).

    Article  ADS  Google Scholar 

  17. D. Meyer, S. Boblest, and G. Wunner, Phys. Rev. A 87, 032515 (2013).

    Article  ADS  Google Scholar 

  18. M. V. Ivanov and P. Schmelcher, Phys. Rev. A 61, 022505 (2000).

    Article  ADS  Google Scholar 

  19. M. V. Ivanov and P. Schmelcher, Phys. Rev. A 60, 3558 (1999).

    Article  ADS  Google Scholar 

  20. M. V. Ivanov and P. Schmelcher, Eur. J. Phys. D 14, 279 (2001).

    Article  ADS  Google Scholar 

  21. M. V. Ivanov and P. Schmelcher, J. Phys. B 34, 2031 (2001).

    Article  ADS  Google Scholar 

  22. M. V. Ivanov and P. Schmelcher, Phys. Rev. A 57, 3793 (1998).

    Article  ADS  Google Scholar 

  23. W. Becken, P. Schmelcher, and F. K. Diakonos, J. Phys. B 32, 1557 (1999).

    Article  ADS  Google Scholar 

  24. W. Becken and P. Schmelcher, J. Phys. B 33, 545 (2000).

    Article  ADS  Google Scholar 

  25. W. Becken and P. Schmelcher, Phys. Rev. A 63, 053412 (2001).

    Article  ADS  Google Scholar 

  26. W. Becken and P. Schmelcher, Phys. Rev. A 65, 033416 (2002).

    Article  ADS  Google Scholar 

  27. O. A. Al-Hujaj and P. Schmelcher, Phys. Rev. A 67, 023403 (2003).

    Article  ADS  Google Scholar 

  28. O. A. Al-Hujaj and P. Schmelcher, Phys. Rev. A 68, 053403 (2003).

    Article  ADS  Google Scholar 

  29. R. Gonzalez-Ferez and P. Schmelcher, Eur. J. Phys. D 23, 189 (2003).

    Article  ADS  Google Scholar 

  30. M. D. Jones, G. Ortiz, and D. M. Ceperley, Phys. Rev. A 54, 219 (1996).

    Article  ADS  Google Scholar 

  31. S. Boblest, C. Schimeczek, and G. Wunner, Phys. Rev. A 89, 012505 (2014).

    Article  ADS  Google Scholar 

  32. S. B. Doma and F. N. El-Gammal, Acta Phys. Polon. A 122 (1), 42 (2012).

    Article  Google Scholar 

  33. S. B. Doma and F. N. El-Gammal, J. Theor. Appl. Phys. 6, 28 (2012).

    Article  ADS  Google Scholar 

  34. S. B. Doma, M. O. Shaker, A. M. Farag, and F. N. El-Gammal, Acta Phys. Polon. A 126, 700 (2014).

    Article  Google Scholar 

  35. N. Metropolis, A. W. Rosenbluth, N. M. Rosenbluth, A. M. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).

    Article  ADS  Google Scholar 

  36. S. Pottorf, A. Puzer and M. Y. Chou, Eur. J. Phys. 20, 205 (1999).

    Article  Google Scholar 

  37. R. W. Hamming, Numerical Methods for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1973).

    MATH  Google Scholar 

  38. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

    MATH  Google Scholar 

  39. S. Larsson, Phys. Rev. 169, 49 (1968).

    Article  ADS  Google Scholar 

  40. M. B. Ruiz, Int. J. Quantum Chem. 101, 246 (2005).

    Article  Google Scholar 

  41. M. Puchalski and K. Pachucki, Phys. Rev. A 73, 022503 (2006).

    Article  ADS  Google Scholar 

  42. N. L. Guevara, F. E. Harris and A. V. Turbiner, Int. J. Quantum Chem. 109, 3036 (2009).

    Article  ADS  Google Scholar 

  43. D. Ruenn Su, Chin. J. Phys. 27, 157 (1989).

    Google Scholar 

  44. O. A. Al-Hujaj and P. Schmelcher, Phys. Rev. A 70, 033411 (2004).

    Article  ADS  Google Scholar 

  45. Z. C. Yan and G. Drake, Phys. Rev. A 52, 3711 (1995).

    Article  ADS  Google Scholar 

  46. X. Guan and B. Li, Phys. Rev. A 63, 043413 (2001).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Alexandria University, Alexandria, 21526, Egypt

    S. B. Doma

  2. Mathematics Department, Faculty of Science, Tanta University, Tanta, 31527, Egypt

    M. O. Shaker & A. M. Farag

  3. Mathematics Department, Faculty of Science, Menofia University, Shebin El-Kom, 32511, Egypt

    F. N. El-Gammal

Authors
  1. S. B. Doma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. O. Shaker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. M. Farag
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. N. El-Gammal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. B. Doma.

Additional information

Published in Russian in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 151, No. 1, pp. 5–14.

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Doma, S.B., Shaker, M.O., Farag, A.M. et al. Variational Monte Carlo calculations of lithium atom in strong magnetic field. J. Exp. Theor. Phys. 124, 1–9 (2017). https://doi.org/10.1134/S1063776117010034

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776117010034

Search

Navigation