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The relativistic bound states of a non-central potential

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

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

    Google Scholar 

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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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Authors and Affiliations

  1. Yang Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    MAHDI ESHGHI

  2. Department of Physics, University of Semnan, Semnan, Iran

    HOSSEIN MEHRABAN

  3. Department of Physics, Faculty of Science, an-Najah National University, Nablus, Palestine

    SAMEER M IKHDAIR

  4. Department of Electrical Engineering, Near East University, Nicosia, Northern Cyprus, Mersin 10, Turkey

    SAMEER M IKHDAIR

Authors
  1. MAHDI ESHGHI
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  2. HOSSEIN MEHRABAN
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  3. SAMEER M IKHDAIR
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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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  • DOI: https://doi.org/10.1007/s12043-017-1375-2

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