The relativistic bound states of a non-central potential

Abstract

We investigate the relativistic effects of a moving particle in the field of a pseudoharmonic oscillatory ring-shaped potential under the spin and pseudospin symmetric Dirac wave equation. We obtain the bound-state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of supersymmetric quantum mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are also studied. Our numerical results for the energy eigenvalues are also presented.

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References

  1. [1]

    G -F Wei and S -H Dong, Euro. Phys. Lett. 87, 40004 (2009)

    ADS  Article  Google Scholar 

  2. [2]

    M -C Zhang and G -Q Huang-Fu, Ann. Phys. 327, 841 (2012)

    ADS  Article  Google Scholar 

  3. [3]

    M Eshghi, M Hamzavi, and S M Ikhdair, Adv. High Energy Phys. 2012, 873619 (2012)

    Article  Google Scholar 

  4. [4]

    M Hamzavi, M Eshghi, and S M Ikhdair, J. Math. Phys. 53, 082101 (2012)

    ADS  Article  MathSciNet  Google Scholar 

  5. [5]

    M Eshghi and H Mehraban, Chin. J. Phys. 50, 4, 533 (2012)

    Google Scholar 

  6. [6]

    P R Page, T Goldman, and J N Ginocchio, Phys. Rev. Lett. 86, 204 (2001)

    ADS  Article  Google Scholar 

  7. [7]

    A Arima, M Harvery, and K Shinizu, Phys. Lett. B 30, 517 (1969)

    ADS  Article  Google Scholar 

  8. [8]

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

    ADS  Article  Google Scholar 

  9. [9]

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

    ADS  Article  Google Scholar 

  10. [10]

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

    ADS  Article  Google Scholar 

  11. [11]

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

    ADS  Article  Google Scholar 

  12. [12]

    A E Stuchbery, J. Phys. G 25, 611 (1999)

    ADS  Article  Google Scholar 

  13. [13]

    A E Stuchbery, Nucl. Phys. A 700, 83 (2002)

    ADS  Article  Google Scholar 

  14. [14]

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

    ADS  Article  Google Scholar 

  15. [15]

    F S Stephens et al, Phys. Rev. Lett. 65, 301 (1990)

    ADS  Article  Google Scholar 

  16. [16]

    F S Stephens et al, Phys. Rev. C 57, R1565 (1998)

    ADS  Article  Google Scholar 

  17. [17]

    D Troltenier, C Bahri, and J P Draayer, Nucl. Phys. A 53, 586 (1995)

    Google Scholar 

  18. [18]

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

    ADS  Article  Google Scholar 

  19. [19]

    J N Ginocchio, Phys. Rev. C 69, 034318 (2004)

    ADS  Article  Google Scholar 

  20. [20]

    J N Ginocchio, Phys. Rep. 414, 165 (2005)

    ADS  Article  MathSciNet  Google Scholar 

  21. [21]

    H Taeli, I Erhan, and Ö Uur, J. Math. Chem. 32, 323 (2002)

    Article  MathSciNet  Google Scholar 

  22. [22]

    C -Y Chen and S -H Dong, Phys. Lett. A 335, 374 (2005)

    ADS  Article  MathSciNet  Google Scholar 

  23. [23]

    M Kocak and B Gönül, Mod. Phys. Lett. A 20, 355 (2005)

    ADS  Article  Google Scholar 

  24. [24]

    J Y Guo, J C Han, and R D Wang, Phys. Lett. A 353, 378 (2006)

    ADS  Article  MathSciNet  Google Scholar 

  25. [25]

    A D Souza Dutra and M Hott, Phys. Lett. A 356, 215 (2006)

    ADS  Article  MathSciNet  Google Scholar 

  26. [26]

    S M Ikhdair and R Sever, Cent. Eur. J. Phys. 6, 685 (2008)

    Google Scholar 

  27. [27]

    S M Ikhdair and R Sever, Int. J. Theor. Phys. 46, 2384 (2007)

    Article  Google Scholar 

  28. [28]

    Y -F Chng and T -Q Dai, Int. J. Mod. Phys. A 23, 1919 (2008)

    ADS  Article  Google Scholar 

  29. [29]

    M -C Zhang, G -H Sun, and S -H Dong, Phys. Lett. A 374, 704 (2010)

    ADS  Article  MathSciNet  Google Scholar 

  30. [30]

    Y -J Xiao and Z -W Long, Commun. Theor. Phys. 53, 54 (2010)

    ADS  Article  Google Scholar 

  31. [31]

    X -Y Gu, M Zhang, and J -Q Sun, Mod. Phys. Lett. B 24, 1759 (2010)

    ADS  Article  Google Scholar 

  32. [32]

    C Chang-Yuan, L Fa-Lin, and S Dong-Sheng, Commun. Theor. Phys. 45, 889 (2006)

    ADS  Article  Google Scholar 

  33. [33]

    C Berkdemir and R Sever, J. Phys. A: Math. Theor. 41, 045302 (2008)

    ADS  Article  Google Scholar 

  34. [34]

    C Berkdemir and Y -F Cheng, Phys. Scr. 79, 035003 (2009)

    ADS  Article  Google Scholar 

  35. [35]

    X -Q Hu, G Luo, Z -M Wu, L -B Niu, and Y Ma, Commun. Theor. Phys. 53, 242 (2010)

    ADS  Article  Google Scholar 

  36. [36]

    R Lisboa, M Malheiro, A S De Castro, P Alberto, and M Fiol-Hais, Phys. Rev. C 69, 024319 (2004)

    ADS  Article  Google Scholar 

  37. [37]

    H Akcay, Phys. Lett. A 373, 616 (2009)

    ADS  Article  MathSciNet  Google Scholar 

  38. [38]

    F Cooper and B Freedman, Ann. Phys. (N.Y.) 146, 262 (1983)

    ADS  Article  Google Scholar 

  39. [39]

    F Cooper, A Khare, and U Sukhatme, Phys. Rep. 251, 267 (1995)

    ADS  Article  MathSciNet  Google Scholar 

  40. [40]

    G Junker, Supersymmetric methods in quantum and statistical physics (Springer, Berlin, 1996)

    Book  MATH  Google Scholar 

  41. [41]

    R Dutt, A Khare, and U P Sukhatme, Am. J. Phys. 56, 2, 163 (1988)

    ADS  Article  Google Scholar 

  42. [42]

    L Gendenshtein, JETP Lett. 38, 356 (1983)

    ADS  Google Scholar 

  43. [43]

    R Dutt, A Khare, and P Sukhatme, Phys. Lett. B 181, 295 (1986)

    ADS  Article  Google Scholar 

  44. [44]

    C -S Jia, X -L Zeng, S -C Li, L -T Sun, and Q -B Yang, Commun. Theor. Phys. 37, 523 (2002)

    Article  Google Scholar 

  45. [45]

    J Maluck, An introduction to supersymmetric quantum mechanics and shape invariant potentials, Thesis of Amsterdam University College (2013)

  46. [46]

    R K Pathria, Statistical mechanics, 1st edn (Pergamon Press, Oxford, 1972)

    Google Scholar 

Download references

Acknowledgement

The authors would like to thank the kind referee(s) for positive and invaluable suggestions which have greatly improved the manuscript.

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Correspondence to MAHDI ESHGHI.

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ESHGHI, M., MEHRABAN, H. & IKHDAIR, S.M. The relativistic bound states of a non-central potential. Pramana - J Phys 88, 73 (2017). https://doi.org/10.1007/s12043-017-1375-2

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Keywords

  • Dirac wave equation
  • supersymmetric quantum mechanics formalism
  • pseudoharmonic oscillatory ring-shaped potential.

PACS Nos

  • 03.65.Pm
  • 03.65.Ge
  • 02.30.Gp