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Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

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Abstract

The Hellmann potential is simply a superposition of an attractive Coulomb potential −a/r plus a Yukawa potential be−δr/r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.

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References

  1. O Haxel, J H D Jensen and H E Suess, Phys. Rev. 75, 1766 (1949)

  2. M Goeppert-Mayer, Phys. Rev. 75, 1969 (1949)

  3. K T Hecht and A Adler, Nucl. Phys. A 137, 129 (1969)

  4. A Arima, M Harvey and K Shimizu, Phys. Lett. B 30, 517 (1969)

  5. A Bohr, I Hamamoto and B R Mottelson, Phys. Scr. 26, 267 (1982)

  6. J Dudek, W Nazarewicz, Z Szymanski and G A Leander, Phys. Rev. Lett. 59, 1405 (1987)

  7. W Nazarewicz, P J Twin, P Fallon and J D Garrett, Phys. Rev. Lett. 64, 1654 (1990)

  8. D Troltenier, W Nazarewicz, Z Szymanski and J P Draayer, Nucl. Phys. A 567, 591 (1994)

  9. J N Ginocchio, Phys. Rev. Lett. 78, 436 (1997)

  10. J Meng, K Sugawara-Tanabe, S Yamaji, P Ring and A Arima, Phys. Rev. C 58, R628 (1998)

  11. P Alberto, M Fiolhais, M Malheiro, A Delfino and M Chiapparini, Phys. Rev. Lett. 86, 5015 (2001)

  12. P Alberto, M Fiolhais, M Malheiro, A Delfino and M Chiapparini, Phys. Rev. C 65, 034307 (2002)

  13. R Lisboa, M Malheiro, P Alberto, M Fiolhais and A S de Castro, Phys. Rev. C 81, 064324 (2010)

  14. S Marcos, M Lopez-Quelle, R Niembro, I N Savushkin and P Bernardos, Phys. Lett. B 513, 30 (2001)

  15. S Marcos, M Lopez-Quelle, R Niembro and I N Savushkin, Eur. Phys. J. A 37, 251 (2008)

  16. H Z Liang, P W Zhao, Y Zhang, J Meng and N V Giai, Phys. Rev. C 83, 041301(R) (2011)

  17. J N Ginocchio, J. Phys. Conf. Ser. 267, 012037 (2011)

  18. J-Y Guo, Phys. Rev. C 85, 021302(R) (2012)

  19. S-WChen and J-Y Guo, Phys. Rev. C 85, 054312 (2012)

  20. H Hellmann, Acta Physicochim. URSS 1, 913 (1935); Acta Physicochim. URSS 4, 225 (1936); Acta Physicochim. URSS 4, 324 (1936); J. Chem. Phys. 3, 61 (1935)

  21. H Hellmann and W Kassatotchkin, Acta Physicochim. URSS 5, 23 (1936) H Hellmann and W Kassatotchkin, J. Chem. Phys. 4, 324 (1936)

  22. P Gombas, Die Statistische Theorie des Atoms und ihre Anwendungen (Springer, Berlin, 1949), p. 304

  23. J Callaway, Phys. Rev. 112, 322 (1958) G J Iafrate, J. Chem. Phys. 45, 1072 (1966) J Callaway and P S Laghos, Phys. Rev. 187, 192 (1969) J McGinn, J. Chem. Phys. 53, 3635 (1970)

  24. V K Gryaznov, Zh. Eksp. Teor. Fiz. 78, 573 (1980), [Sov. Phys.-JETP 51, 288 (1980)]

  25. V A Alekseev, V E Fortov and I T Yakubov, Usp. Fiz. Nauk 139, 193 (1983), [Sov. Phys.-Usp. 26, 99 (1983)]

  26. Y P Varshni and R C Shukla, Rev. Mod. Phys. 35, 130 (1963)

  27. J N Das and S Chakravarty, Phys. Rev. A 32, 176 (1985)

  28. J Adamowski, Phys. Rev. A 31, 43 (1985)

  29. R Dutt, U Mukherji and Y P Varshni, Phys. Rev. A 34, 777 (1986)

  30. R L Hall and Q D Katatbeh, Phys. Lett. A 287, 183 (2001)

  31. S M Ikhdair and R Sever, Int. J. Mod. Phys. A 21, 6465 (2006)

  32. S M Ikhdair and R Sever, J. Mol. Struct.: Theochem. 809, 103 (2007)

  33. A K Roy, A F Jalbout and I E Proynov, J. Math. Chem. 44, 260 (2008)

  34. I Nasser and M S Abdelmonem, Phys. Scr. 83, 055004 (2011)

  35. A F Nikiforov and V B Uvarov, Special functions of mathematical physics (Birkhausr, Berlin, 1988)

  36. M G Miranda, G H Sun and S H Dong, Int. J. Mod. Phys. E 19, 123 (2010) M C Zhang, G H Sun and S H Dong, Phys. Lett. A 374, 704 (2010)

  37. S M Ikhdair, Int. J. Mod. Phys. C 20(1), 25 (2009) C Tezcan and R Sever, Int. J. Theor. Phys. 48, 337 (2009)

  38. W Greiner. Relativistic quantum mechanics, wave equations, Third Edition (Springer, 2000)

  39. S G Zhou, J Meng and P Ring, Phys. Rev. Lett. 91, 262501 (2003)

  40. X T He, S G Zhou, J Meng, E G Zhao and W Scheid, Eur. Phys. J. A 28, 265 (2006)

  41. C Y Song, J M Yao and J Meng, Chin. Phys. Lett. 26, 122102 (2009)

  42. C Y Song and J M Yao, Chin. Phys. C 34, 1425 (2010)

  43. R L Greene and C Aldrich, Phys. Rev. A 14, 2363 (1976)

  44. M Hamzavi, K-E Thylwe and A A Rajabi, Commun. Theor. Phys. 60, 1 (2013)

  45. S M Ikhdair, Phys. Scr. 83, 015010 (2011)

  46. S M Ikhdair and R Sever, Phys. Scr. 79, 035002 (2009)

  47. S M Ikhdair and R Sever, Ann. Phys. 17, 897 (2008)

  48. M R Setare and S Haidari, Phys. Scr. 81, 065201 (2010)

  49. M Hamzavi, M Movahedi, K-E Thylwe and A A Rajabi, Chin. Phys. Lett. 29, 080302 (2012)

  50. J N Ginocchio, Phys. Rep. 315, 231 (1999)

  51. J N Ginocchio, Nucl. Phys. A 663c, 654 (1999)

  52. J Meng, K Sugawara-Tanabe, S Yamaji and A Arima, Phys. Rev. C 59, 154 (1999)

  53. H Liang, S Shen, P Zhao and J Meng, Phys. Rev. C 014334, 87 (2013)

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Acknowledgements

The authors thank the anonymous referee for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran

    M HAMZAVI

  2. Department of Physic, Faculty of Science, an-Najah National University, Nablus, West Bank, Palestine

    S M IKHDAIR

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  1. M HAMZAVI
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  2. S M IKHDAIR
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Correspondence to M HAMZAVI.

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HAMZAVI, M., IKHDAIR, S.M. Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries. Pramana - J Phys 83, 49–61 (2014). https://doi.org/10.1007/s12043-014-0764-z

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  • DOI: https://doi.org/10.1007/s12043-014-0764-z

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