10.57647/j.jtap.2025.1905.44

Approximate Solutions of The Dirac Equation with Screened Kratzer-Hellmann Problem Including Generalized Tensor Interaction

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  • Uduakobong S. Okorie*1,
  • Gaotsiwe J. Rampho1,
  • Makgamathe J. Sithole1,
  • Morris Ramtswana1,
  • Akpan N. Ikot2,3,
  1. Department of Physics, University of South Africa, Florida 1710, Johannesburg, South Africa
  2. Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Nigeria
  3. Western Caspian University, Baku, Azerbaijan

Received: 2025-03-14

Revised: 2025-06-24

Accepted: 2025-08-22

Published in Issue 2025-09-30

Copyright (c) 2025 Uduakobong S. Okorie, Gaotsiwe J. Rampho, Makgamathe J. Sithole, Morris Ramtswana, Akpan N. Ikot (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Okorie US, Rampho GJ, Sithole MJ, Ramtswana M, Ikot AN. Approximate Solutions of The Dirac Equation with Screened Kratzer-Hellmann Problem Including Generalized Tensor Interaction. J Theor Appl phys. 2025 Sep. 30;19(5). Available from: https://oiccpress.com/jtap/article/view/17681
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Abstract

The Dirac equation presents better perspective of understanding the motion of particles in region of relativistic quantum mechanics. In this regard, we examine the approximate bound state solutions of the Dirac equation under the spin and pseudospin symmetries for the screened Kratzer-Hellmann potential including generalized tensor interaction. By using the Nikiforov-Uvarov functional analysis method and an approximation scheme, the analytical, numerical and graphical energies of the combined potential were obtained for both symmetries, for different quantum numbers. Degeneracies were observed in the energy values in the absence of the generalized tensor interaction and these degeneracies were removed with the help of the generalized tensor interaction, which is made up of the Coulomb, the Yukawa and the Hulthen potentials. The variations of the energy eigenvalues with screening parameter for spin and pseudospin symmetries were studied for various values of the quantum numbers. The increase and decrease of the energy eigenvalues are observed for both symmetries, indicating tightly bound and loosely bound states, respectively. Our study shows that the obtained energies are very sensitive to the screening parameter and quantum numbers.

Keywords

  • Dirac equation,
  • Energy eigenvalues,
  • Generalized tensor interaction,
  • Degeneracy,
  • Nikiforov-Uvarov functional analysis method
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References

  1. A. Gallerati, Eur. Phys. J. Plus. 134(5), 202 (2019).
  2. F. Romeo, Eur. Phys. J. Plus. 135(6), 1 (2020).
  3. A. Chenaghlou, S. Aghaei and N. G. Niari, Eur. Phys. J. D. 75, 139 (2021).
  4. S. Massoudi, M. Amniat-Talab, S. Aghaei, M. Razazian, E. Ahmadi and J. Rahighi, J.
  5. S. Massoudi, S. Aghaei, M. Amniat-Talab and J. Rahighi, Pramana J. Phys. 94, 158 (2020).
  6. C. S. Jia, L. H. Zhang and J. Y. Liu, Eur. Phys. J. Plus. 131, 2 (2016).
  7. S. H. Dong, W. C. Qiang, G. H. Sun and V. B. Bezerra, J. Phys. A Math. Theor. 40, 10535 (2007).
  8. P. Zhang, H. C. Long and C. S. Jia, Eur. Phys. J. Plus. 131, 117 (2016).
  9. Z. W. Shui and C. S. Jia, Eur. Phys. J. Plus. 132, 292 (2017).
  10. Z. W. Shui and C. S. Jia, Eur. Phys. J. Plus. 131, 215 (2016).
  11. Y. Sun, G. D. Zhang and C. H. Jia, Chem. Phys. Lett. 636, 197 (2015).
  12. A. Kurniawan, A. Suparmi and A. Cari, Chin. Phys. B 24, 030302 (2015).
  13. H. Bakhti, A. Diaf and M. Hachama, Phys. Scr. 94, 055204 (2019).
  14. H. Bakhti, A. Diaf and M. Hachama, Comput. Theor. Chem. 1185, 112879 (2020).
  15. A. Diaf, M. Hachama and M. M. H. Ezzine, Phys. Scr. 96(10), 105212 (2021).
  16. M. M. H. Ezzine, M. Hachama and A. Diaf, Phys. Scr. 96(12), 125260 (2021).
  17. A. Diaf, M. Hachama and M. M’hamed Ezzine, Mol. Phys. 121(6), e2198045 (2023).
  18. A. I. Ahmadov, S. M. Nagiyev, C. Aydin, V. A. Tarverdiyeva, M. Sh. Orujova and S. V.Badalov, Eur. Phys. J. Plus. 137, 1075 (2022).
  19. A. Durmus, Few-Body Syst. 59, 7 (2018).
  20. U. S. Okorie, E. E. Ibekwe, M. C. Onyeaju and A. N. Ikot, Eur. Phys. J. Plus. 133, 433 (2018).
  21. I. B. Okon, E. Omugbe, A. D. Antia, C. A. Onate, L. E. Akpabio and O. E. Osafile, Sci. Rep. 11, 1 (2021).
  22. H. Chen, Z. W. Long, Y. Yang and C. Y. Long, Mod. Phys. Lett. A 35, 2050179 (2020).
  23. N. Messai, B. Hamil and A. Hafdallah, Mod. Phys. Lett. A 33, 1850202 (2018).
  24. H. Bada and M. Aouachria, Mod. Phys. Lett. A 34, 1950246 (2019).
  25. A. Chenaghlou, S. Aghaei and R. Mokhtari, Pramana J. Phys. 94, 151 (2020).
  26. V. Dzhunushaliev, V. Folomeev and A, Serikbolova, Phys. Lett. B 806, 135480 (2020).
  27. R. Mokhtari, R. H. Sani and A. Chenaghlou, Eur. Phys. J. Plus, 134, 446 (2019).
  28. S. Dong, J. Garcia-Ravelo and S. H. Dong, Phys. Scr. 76, 393 (2007).
  29. F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
  30. H. Ciftci, R. L. Hall and N. Saad, J. Phys. A: Math. Gen. 36, 11807 (2003).
  31. A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics.
  32. S. H. Dong, Factorization Method in Quantum Mechanics. Springer (2007).
  33. J. N. Ginocchio, Phys. Rep. 414, 165 (2005).
  34. S. G. Zhou, J. Meng and P. Ring, Phys. Rev. Lett. 91, 262501 (2003).
  35. C. A. Onate, O. Adebimpe, A. F. Lukman, J. O. Okoro and M. O. Olowayemi, J. Kor. Phys. Soc. 74(3), 205 (2019).
  36. A. Tas, Eur. Phys. J. Plus 139, 361 (2024).
  37. H. H. Karayer, D. Demirhan, C. Aydin and A. I. Ahmadov Appl. Comput. Math. 23(4), 437 (2024).
  38. C. A. Onate, I. B. Okon, E. Omugbe, A. Basem, B. F. Castillo Parra, K. O. Emeje, J. A.
  39. Owolabi and A. R. Obasuyi, Sci. Rep. 14, 9583 (202
  40. H. A. Abdallah and H. Y. Abdullah, AIP Conf. Proc. 1718, 090001 (2016).
  41. H. Y. Abdullah and C. T. Londhe, Iran J. Sci. Techn. Trans. Sci. 43, 1361 (2019).
  42. M. H. Mohammadi, R. Bhaskaran, H. Y. Abdullah, H. A. Abdallah, G. Biskos and S. Bhowmick, Int. J. Quant. Chem. 124, e27288 (2024)
  43. A. Maireche, Rev. Mex. Fís. 68(2), 020801-1 (2022).
  44. A. Maireche, Mod. Phys. Lett. A, 36(33), 2150232 (2021).
  45. A. Maireche, Int. J. Geom. Meth. Mod. Phys. 20(14), 2450016 (2023).
  46. G. T. Osobonye, U. S. Okorie, P. O. Amadi and A. N. Ikot. Can. J. Phys. 99(7), 583 (2021).
  47. A. N. Ikot, E. Maghsoodi, H. Hassanabadi and J. A. Obu, J. Kor. Phys. Soc. 64(9), 1248
  48. C. A. Onate, M. C. Onyeaju, A. N. Ikot, O. Ebomwonyi and J. O. A. Idiodi, Commun. Theor. Phys. 70, 294 (2018).
  49. V. G. Bagrov, Russ. Phys. J. 61, 403 (2018).
  50. M. G. Garcia, S. Pratapsi, P. Alberto and A. S. de Castro, Phys. Rev. A 99, 062102 (2019).
  51. A. N. Ikot, U. S. Okorie, P. O. Amadi, C. O. Edet, G. J. Rampho and R. Sever, Few- Body Syst. 62, 9 (2021).
  52. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics. McGraw-Hill. New York (1964)
  53. J. Meng, K. Sugawara-Tanabe, S. Yamaji and A. Arima, Phys. Rev. C 59, 154 (1999).
  54. R. L. Greene and C. Aldrich, Phys. Rev. A 14, 2363 (1976).
  55. I. B. Okon, E. Omugbe, A. D. Antia, C. A. Onate, L. E. Akpabio and O. E. Osafile Sci. Rep. 11, 892 (2021).
  56. A. N. Ikot, E. Maghsoodi, E. J. Ibanga, S. Zarrinkamar and H. Hassanabadi, Chin. Phys. B, 12, 120302 (2013).
  57. A. N. Ikot, H. Hassanabadi and T. M. Abbey, Commun. Theor. Phys. 64, 637 (2015).
  58. S. Zare, H. Hassanabadi, G. J. Rampho and A. N. Ikot, Eur. Phys. J. Plus. 135, 748 (2020).
  59. C. Tezcan and R. Sever, Int. J. Theor. Phys. 48, 337 (2008).
  60. B. J. Falaye, K. J. Oyewumi, S. M. Ikhdair and M. Hamzavi, Phys. Scr. 89, 115204 (2014).
  61. C. Berkdemir, Application of the Nikiforov–Uvarov method in quantum mechanics, in Theoretical Concept of Quantum Mechanics, vol. 11, ed. by M.R. Pahlavani, InTech, Rijeka (2012).