Skip to main content
SpringerLink
Log in

Spin and pseudospin symmetries of a relativistic fermion in an elastic medium with spiral dislocations

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In this study, we investigate a relativistic fermion in an elastic medium as well as a linear topological defect by focusing on the spiral dislocation. Then, we solve the coupled Dirac equation in the presence of scalar and vector potentials. We investigate two special cases by focusing on a spin symmetry limit and a pseudospin symmetry limit. After considering a fermion based on the Dirac equation in the background of spiral dislocation, by considering two special cases, in the presence of oscillator and Kratzer-like potentials, we find the energy eigenvalues according to the wave functions by using of analytical methods.

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. R.A. Puntigam, H.H. Soleng, Class. Quantum Grav. 14, 1129 (1997). https://doi.org/10.1088/0264-9381/14/5/017

    Article  ADS  Google Scholar 

  2. H. Kleinert, Gauge Fields in Condensed Matter, vol. 2 (World Scientific, Singapore, 1989)

    Book  Google Scholar 

  3. I.E. Dzyaloshinskii, G.E. Volovick, Ann. Phys. 125, 67 (1980). https://doi.org/10.1016/0003-4916(80)90119-0

    Article  ADS  Google Scholar 

  4. R. Bausch, R. Schmitz, L.A. Turski, Phys. Rev. Lett 80, 2257 (1998). https://doi.org/10.1103/PhysRevLett.80.2257

    Article  ADS  Google Scholar 

  5. M.O. Katanaev, I.V. Volovich, Ann. Phys. 216, 1 (1992). https://doi.org/10.1016/0003-4916(52)90040-7

    Article  ADS  Google Scholar 

  6. A.L.S. Netto, C. Furtado, J. Phys. Condens. Matter 20, 125209 (2008). https://doi.org/10.1088/0953-8984/20/12/125209

    Article  ADS  Google Scholar 

  7. A.V.D.M. Maia, K. Bakke, Eur. Phys. J. C 79, 551 (2019). https://doi.org/10.1140/epjc/s10052-019-7067-y

    Article  ADS  Google Scholar 

  8. J. Sólyom, Fundamentals of the Physics of Solids, Volume 1: Structure and Dynamics (Springer, Berlin, 2006). ISBN:978-3-540-72599-2

  9. A.E. Romanov, V.I. Vladimiro, Physica Status Solidi (a) 78, 11 (1983). https://doi.org/10.1002/pssa.2210780102

    Article  ADS  Google Scholar 

  10. K.C. Valanis, V.P. Panoskaltsis, Acta Mech. 175, 77 (2005). https://doi.org/10.1007/s00707-004-0196-9

    Article  Google Scholar 

  11. R.L.L. Vitória, K. Bakke, Eur. Phys. J. Plus 133, 490 (2018). https://doi.org/10.1140/epjp/i2018-12310-9

    Article  Google Scholar 

  12. K. Bakke, C. Furtado, Phys. Rev. A 87, 012130 (2013). https://doi.org/10.1103/PhysRevA.87.012130

    Article  ADS  Google Scholar 

  13. A.V.D.M. Maia, K. Bakke, Physica B 531, 213 (2018). https://doi.org/10.1016/j.physb.2017.12.045

    Article  ADS  Google Scholar 

  14. S. Zare, H. Hassanabadi, M. de Montigny, Eur. Phys. J. Plus 135, 122 (2020). https://doi.org/10.1140/epjp/s13360-020-00184-3

    Article  Google Scholar 

  15. C. Furtado, V.B. Bezerra, F. Moraes, Phys. Lett. A 289, 160 (2001). https://doi.org/10.1016/S0375-9601(01)00615-6

    Article  ADS  Google Scholar 

  16. G. de Aarques, C. Furtado, V.B. Bezerra, F. Moraes, J. Phys. A Math. Gen. 34, 5945 (2001). https://doi.org/10.1088/0305-4470/34/30/306

    Article  ADS  Google Scholar 

  17. C. Furtado, F. Moraes, Europhys. Lett. 45, 279 (1999). https://doi.org/10.1209/epl/i1999-00159-8

    Article  ADS  Google Scholar 

  18. C. Furtado, F. Moraes, J. Phys. A Math. Gen. 33, 5513 (2000). https://doi.org/10.1088/0305-4470/33/31/306

    Article  ADS  Google Scholar 

  19. V.B. Bezerra, J. Math. Phys 38, 2553 (1997). https://doi.org/10.1063/1.531995

    Article  MathSciNet  ADS  Google Scholar 

  20. X.C. Zhang, Q.W. Liu, C.S. Jia, L.Z. Wang, Phys. Lett. A 340, 59 (2005). https://doi.org/10.1016/j.physleta.2005.04.011

    Article  ADS  Google Scholar 

  21. P. Schluter, K.-H. Wietschorke, W. Greiner, J. Phys. A Math. Gen. 16, 1999 (1983). https://doi.org/10.1088/0305-4470/16/9/024

    Article  ADS  Google Scholar 

  22. A.W. Thomas, W. Weise, Structure of the Nucleon (Wiley, Berlin, 2001)

    Book  Google Scholar 

  23. B. Thaller, The Dirac Equation (Springer, New York, 1992)

    Book  Google Scholar 

  24. M. Moshinsky, A. Szczepaniak, J. Phys. A Math. Gen. 22, L817 (1988). https://doi.org/10.1088/0305-4470/22/17/002

    Article  Google Scholar 

  25. D. Itô, K. Mori, E. Carrieri, Nuovo Cimento A 51, 1119 (1967). https://doi.org/10.1007/BF0272

    Article  ADS  Google Scholar 

  26. M. de Montigny, S. Zare, H. Hassanabadi, Gen. Relativ. Gravit. 50, 47 (2018). https://doi.org/10.1007/s10714-018-2370-8

    Article  ADS  Google Scholar 

  27. C. Quesne, M. Moshinsky, J. Phys. A Math. Gen. 23, 2263 (1990). https://doi.org/10.1088/0305-4470/23/12/011

    Article  ADS  Google Scholar 

  28. M. Hosseinpour, H. Hassanabadi, M. de Montigny, Eur. Phys. J. C 79, 311 (2019). https://doi.org/10.1140/epjc/s10052-019-6830-4

    Article  ADS  Google Scholar 

  29. K. Bakke, C. Furtado, Ann. Phys. 336, 489 (2013). https://doi.org/10.1016/j.aop.2013.06.007

    Article  ADS  Google Scholar 

  30. J. Carvalho, C. Furtado, F. Moraes, Phys. Rev. A 84, 032109 (2011). https://doi.org/10.1103/PhysRevA.84.032109

    Article  ADS  Google Scholar 

  31. K. Bakke, Eur. Phys. J. Plus 127, 82 (2012). https://doi.org/10.1140/epjp/i2012-12082-2

    Article  ADS  Google Scholar 

  32. T.Y. Wu, W.Y. Pauchy Hwang. In: Relativistic quantum mechanics and quantum fields (World Scientific, Singapore, 1991). ISBN:978-981-02-0608-6

  33. W. Greiner, Relativistic Quantum Mechanics: Wave Equations (Springer, Berlin, 2000). https://doi.org/10.1007/978-3-642-88082-7

    Book  MATH  Google Scholar 

  34. J.A. Neto, M.J. Bueno, C. Furtado, Ann. Phys. 373, 273 (2016). https://doi.org/10.1016/j.aop.2016.07.023

    Article  ADS  Google Scholar 

  35. K. Bakke, C. Furtado, Phys. Lett. A 376, 1269 (2012). https://doi.org/10.1016/j.physleta.2012.02.044

    Article  ADS  Google Scholar 

  36. M.J. Bueno, J.L. de Melo, C. Furtado, A.M. de M. Carvalho, Eur. Phys. J. Plus (2014). https://doi.org/10.1140/epjp/i2014-14201-5

    Article  Google Scholar 

  37. K. Bakke, H. Mota, Eur. Phys. J. Plus 133, 409 (2018). https://doi.org/10.1140/epjp/i2018-12268-6

    Article  Google Scholar 

  38. M. Hosseinpour, F.M. Andrade, E.O. Silva, H. Hassanabadi, Eur. Phys. J. C 77, 270 (2017). https://doi.org/10.1140/epjc/s10052-017-4834-5

    Article  ADS  Google Scholar 

  39. F. Ahmed, Eur. Phys. J. C 79, 534 (2019). https://doi.org/10.1140/epjc/s10052-019-7029-4

    Article  Google Scholar 

  40. H. Hassanabadi, E. Maghsoodi, S. Zarrinkama, H. Rahimov, Mod. Phys. Lett. A 26, 2703 (2011). https://doi.org/10.1142/S0217732311037091

    Article  ADS  Google Scholar 

  41. A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhäuser, Basel, 1988). https://doi.org/10.1007/978-1-4757-1595-8

    Book  MATH  Google Scholar 

  42. A. Soylu, O. Bayrak, I. Boztosun, J. Phys. A Math. Theor. 41, 065308 (2008). https://doi.org/10.1088/1751-8113/41/6/065308

    Article  ADS  Google Scholar 

  43. R.L.L. Vitória, C. Furtado, K. Bakke, Ann. Phys. 370, 128 (2016). https://doi.org/10.1016/j.aop.2016.03.016

    Article  ADS  Google Scholar 

  44. K. Bakke, C. Furtado, Ann. Phys. 355, 48 (2015). https://doi.org/10.1016/j.aop.2015.01.028

    Article  ADS  Google Scholar 

  45. J. Carvalho, A.M. de M. Carvalho, E. Cavalcante, C. Furtado, Eur. Phys. J. C 76, 365 (2016). https://doi.org/10.1140/epjc/s10052-016-4189-3

    Article  ADS  Google Scholar 

  46. A. Arima, M. Harvey, K. Shimizu, Phys. Lett. B 30, 517 (1969). https://doi.org/10.1016/0370-2693(69)90443-2

    Article  ADS  Google Scholar 

  47. K.T. Hecht, A. Adeler, Nucl. Phys. A 137, 129 (1969). https://doi.org/10.1016/0375-9474(69)90077-3

    Article  ADS  Google Scholar 

  48. G.-F. Wei, S.-H. Dong, Phys. Lett. A 373, 2428 (2009). https://doi.org/10.1016/j.physleta.2009.05.011

    Article  MathSciNet  ADS  Google Scholar 

  49. G.-F. Wei, S.-H. Dong, EPL 87, 40004 (2009). https://doi.org/10.1209/0295-5075/87/40004

    Article  ADS  Google Scholar 

  50. G.-F. Wei, S.-H. Dong, Eur. Phys. J. A 43, 185 (2010). https://doi.org/10.1140/epja/i2009-10901-8

    Article  ADS  Google Scholar 

  51. G.-F. Wei, Z.-Z. Zhen, S.-H. Dong, Cent. Eur. J. Phys 7, 175 (2009). https://doi.org/10.2478/s11534-008-0143-9

    Article  Google Scholar 

  52. G.-F. Wei, S.-H. Dong, Phys. Lett. A 373, 49 (2008). https://doi.org/10.1016/j.physleta.2008.10.064

    Article  MathSciNet  ADS  Google Scholar 

  53. G.-F. Wei, S.-H. Dong, Phys. Scr. 81, 035009 (2010). https://doi.org/10.1088/0031-8949/81/03/035009

    Article  ADS  Google Scholar 

  54. G.-F. Wei, S.-H. Dong, Eur. Phys. J. A 46, 207 (2010). https://doi.org/10.1140/epja/i2010-11031-0

    Article  ADS  Google Scholar 

  55. J.N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997). https://doi.org/10.1103/PhysRevLett.78.436

    Article  ADS  Google Scholar 

  56. J.N. Ginocchio, Phys. Rev. Lett. 95, 252501 (2005). https://doi.org/10.1103/PhysRevLett.95.252501

    Article  ADS  Google Scholar 

  57. J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, A. Arima, Phys. Rev. C 58, R628 (1998). https://doi.org/10.1103/PhysRevC.58.R628

    Article  ADS  Google Scholar 

  58. A.D. Alhaidari, H. Bahlouli, A. Al-Hasan, Phys. Lett. A 349, 87 (2006). https://doi.org/10.1016/j.physleta.2005.09.008

    Article  MathSciNet  ADS  Google Scholar 

  59. C.S. Jia, P. Guo, X.L. Peng, J. Phys. A Math. Theor. 39, 7737 (2006). https://doi.org/10.1088/0305-4470/39/24/010

    Article  ADS  Google Scholar 

  60. Y. Xu, S. He, C.S. Jia, J. Phys. A Math. Theor. 41, 255302 (2008). https://doi.org/10.1088/1751-8113/41/25/255302

    Article  ADS  Google Scholar 

  61. A.N. Ikot, E. Maghsoodi, S. Zarrinkamar, H. Hassanabadi, Few Body Syst. 54, 2027 (2013). https://doi.org/10.1007/s00601-013-0701-6

    Article  ADS  Google Scholar 

  62. N.D. Birrel, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982)

    Book  Google Scholar 

  63. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (IE-Wiley, New York, 1972)

    Google Scholar 

  64. M. Nakahara, Geometry, Topology and Physics (Institute of Physics Publishing, Bristol, 2003)

    MATH  Google Scholar 

  65. E.R.F. Medeirosa, E.R.B. de Mello, Eur. Phys. J. C 72, 2051 (2012). https://doi.org/10.1140/epjc/s10052-012-2051-9

    Article  ADS  Google Scholar 

  66. F.M. Andrade, E.O. Silva, Phys. Lett. B 738, 44 (2014). https://doi.org/10.1016/j.physletb.2014.09.017

    Article  MathSciNet  ADS  Google Scholar 

  67. A.D. Alhaidari, Mod. Phys. Lett. A 21, 581 (2006). https://doi.org/10.1142/S0217732306019049

    Article  MathSciNet  ADS  Google Scholar 

  68. C. Tezcan, R. Sever, Int. J. Theor. Phys. 48, 377 (2009). arXiv:0807.2304v3

    Article  Google Scholar 

  69. R. Van Royen, V.F. Weisskopf, Nuovo Cimento A 50, 617 (1967). https://doi.org/10.1007/BF02823542

    Article  ADS  Google Scholar 

  70. O. Bayrak, I. Boztosun, H. Ciftci, Theor. Comput. Devel. 107, 540 (2007). https://doi.org/10.1002/qua.21141

    Article  Google Scholar 

  71. M.R. Setare, E. Karimi, Phys. Scr. 75, 90 (2007). https://doi.org/10.1088/0031-8949/75/1/015

    Article  MathSciNet  ADS  Google Scholar 

  72. R.L. Hall, N. Saad, K.D. Sen, H. Ciftci, Phys. Rev. A 80, 032507 (2009). https://doi.org/10.1103/PhysRevA.80.032507

    Article  ADS  Google Scholar 

  73. R.L. Hall, N. Saad, K.D. Sen, J. Math. Phys. 51, 022107 (2010). https://doi.org/10.1063/1.3290740

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank the referee for a thorough reading of our manuscript and constructive suggestions. Also the authors would like to thank Professor Abdulaziz Alhaidari, Saudi Center for Theoretical Physics, for many useful comments and suggestions.

Author information

Authors and Affiliations

  1. Faculty of Physics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

    S. Zare & H. Hassanabadi

  2. Department of Physics, University of South Africa, Florida, 1710, Johannesburg, South Africa

    G. J. Rampho & A. N. Ikot

  3. Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Nigeria

    A. N. Ikot

Authors
  1. S. Zare
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Hassanabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. J. Rampho
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. N. Ikot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Hassanabadi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zare, S., Hassanabadi, H., Rampho, G. . et al. Spin and pseudospin symmetries of a relativistic fermion in an elastic medium with spiral dislocations. Eur. Phys. J. Plus 135, 748 (2020). https://doi.org/10.1140/epjp/s13360-020-00779-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00779-w

Search

Navigation