Advertisement

On an approximation of the two-body spinless Salpeter equation

  • Y. CharguiEmail author
Regular Article

Abstract.

In recent years several published works have aimed at finding approximate analytical solutions of the two-body spinless Salpeter equation, starting from the approximation \(\sqrt{p^{2}+m^{2}} \approx p^{2}/2m-p^{4}/8m^{3}\). In this article we show that the approach they used ignores a term of the order \((1/m^{3})\) which should in fact be retained in consonance with the assumed expansion of the kinetic term. We also demonstrate how effects of this term can be reduced in an additional potential using a proper gauge-fixing choice. For illustration, we solve the resulting equation under an exponential potential for s-states and we examine the significance of the extra term for the obtained energy eigenvalues.

References

  1. 1.
    K. Kowalski, J. Rembieliński, Phys. Rev. A 81, 012118 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    K. Kowalski, J. Rembieliński, Phys. Rev. A 84, 012108 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    C. Semay, Phys. Lett. A 376, 2217 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Chargui, A. Dhahbi, A. Trabelsi, Few-Body Syst. 55, 1233 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Chargui, A. Dhahbi, A. Trabelsi, Phys. Scr. 90, 015201 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    W. Lucha, F.F. Schoberl, Int. J. Mod. Phys. A 30, 1550062 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    H. Sobhani, H. Hassanabadi, Adv. High Energy Phys. 2016, 3647392 (2016)CrossRefGoogle Scholar
  8. 8.
    K.-E. Thylwe, Commun. Theor. Phys. 67, 619 (2017)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Y. Chargui, A. Dhahbi, J. Math. Phys. 59, 082304 (2018)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    W. Lucha, F.F. Schoberl, Int. J. Mod. Phys. A 7, 6431 (1992)ADSCrossRefGoogle Scholar
  11. 11.
    C. Semay, B. Silvestre-Brac, Nucl. Phys. A 618, 455 (1997)ADSCrossRefGoogle Scholar
  12. 12.
    F. Brau, C. Semay, Phys. Rev. D 58, 034015 (1998)ADSCrossRefGoogle Scholar
  13. 13.
    F. Brau, C. Semay, B. Silvestre-Brac, Phys. Rev. C 66, 055202 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    E.E. Salpeter, H.A. Bethe, Phys. Rev. 84, 1232 (1951)ADSCrossRefGoogle Scholar
  15. 15.
    E.E. Salpeter, Phys. Rev. 87, 328 (1952)ADSCrossRefGoogle Scholar
  16. 16.
    W. Greiner, J. Reinhardt, Quantum Electrodynamics (Springer-Verlag, Berlin, 1994)Google Scholar
  17. 17.
    W. Lucha, F.F. Schberl, Int. J. Mod. Phys. A 14, 2309 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    J.C. Raynal, S.M. Roy, V. Singh, A. Martin, J. Stubbe, Phys. Lett. B 320, 105 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    F. Brau, Phys. Lett. A 313, 363 (2003)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    R.L. Hall, W. Lucha, F.F. Schöberl, Int. J. Mod. Phys. A 18, 2657 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    Z.F. Li, J.J. Liu, W. Lucha, F.F. Schöberl, J. Math. Phys. 46, 103514 (2005)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    R.L. Hall, W. Lucha, Phys. Lett. A 374, 1980 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    S.M. Ikhdair, R. Sever, Z. Phys. C 56, 155 (1992)ADSCrossRefGoogle Scholar
  24. 24.
    S.M. Ikhdair, R. Sever, Z. Phys. C 58, 153 (1993)ADSCrossRefGoogle Scholar
  25. 25.
    G. Jaczko, L. Durand, Phys. Rev. D 58, 114017 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 19, 1771 (2004)ADSCrossRefGoogle Scholar
  27. 27.
    S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 20, 6509 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. E 17, 1107 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    S. Zarrinkamar, A.A. Rajabi, H. Hassanabadi, Few-Body Syst. 52, 165 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    S. Hassanabadi, M. Ghominejad, B.H. Yazarloo, S. Zarrinkamar, H. Hassanabadi, Chin. Phys. C 37, 083102 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    H. Feizi, M. Hoseininaveh, A.H. Ranjbar, Int. J. Mod. Phys. E 22, 1350039 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    S. Hassanabadi, M. Ghominejad, K.-E. Thylwe, Commun. Theor. Phys. 63, 423 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    H. Panahi, S. Zarrinkamar, M. Baradaran, Eur. Phys. J. Plus 131, 35 (2016)CrossRefGoogle Scholar
  34. 34.
    A. Arda, Indian J. Phys. 91, 903 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    S. Zarrinkamar, Z. Naturforsch. A 71, 1027 (2017)ADSGoogle Scholar
  36. 36.
    O.J. Oluwadare, K.J. Oyewumi, Eur. Phys. J. Plus 132, 277 (2017)CrossRefGoogle Scholar
  37. 37.
    A. Mostafazadeh, J. Math. Phys. 43, 205 (2002)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    D. Beigie, S. Wiggins, Phys. Rev. A 45, 4803 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    H. Taşeli, J. Phys. A 31, 779 (1998)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Physics Department, College of Science and Arts at ArRassQassim UniversityArRassSaudi Arabia
  2. 2.Université de Tunis El Manar, Faculté des Sciences de Tunis, Unité de Recherche de Physique Nucléaire et des Hautes EnergiesTunisTunisia

Personalised recommendations