Skip to main content
Log in

Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for Hulthén-like potential including a Coulomb-like tensor interaction are obtained with any arbitrary spin–orbit coupling number κ using the Pekeris approximation. The generalized parametric Nikiforov–Uvarov (NU) method is used to obtain the energy eigenvalues and the corresponding wave functions in their closed forms. We show that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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. Ginocchio J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414(4–5), 165 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  2. Bohr A., Hamamoto I., Mottelson B.R.: Pseudospin in rotating nuclear potentials. Phys. Scr. 26, 267 (1982)

    Article  ADS  Google Scholar 

  3. Dudek J., Nazarewicz W., Szymanski Z., Leander G.A.: Abundance and systematics of nuclear superdeformed states: relation to the pseudospin and pseudo-SU(3) symmetries. Phys. Rev. Lett. 59, 1405 (1987)

    Article  ADS  Google Scholar 

  4. Troltenier D., Bahri C., Draayer J.P.: Generalized pseudo-SU(3) model and pairing. Nucl. Phys. A 586, 53 (1995)

    Article  ADS  Google Scholar 

  5. Page P.R., Goldman T., Ginocchio J.N.: Relativistic symmetry suppresses quark spin–orbit splitting. Phys. Rev. Lett. 86, 204 (2001)

    Article  ADS  Google Scholar 

  6. Ginocchio J.N., Leviatan A., Meng J., Zhou S.G.: Test of pseudospin symmetry in deformed nuclei. Phys. Rev. C 69, 034303 (2004)

    Article  ADS  Google Scholar 

  7. Ginocchio J.N.: Pseudospin as a relativistic symmetry. Phys. Rev. Lett. 78(3), 436 (1997)

    Article  ADS  Google Scholar 

  8. Hecht K.T., Adler A.: Generalized seniority for favored J ≠ 0 pairs in mixed configurations. Nucl. Phys. A 137, 129 (1969)

    Article  ADS  Google Scholar 

  9. Arima A., Harvey M., Shimizu K.: Pseudo LS coupling and pseudo SU3 coupling schemes. Phys. Lett. B 30, 517 (1969)

    Article  ADS  Google Scholar 

  10. Ikhdair S.M., Sever R.: Solutions of the spatially-dependent mass Dirac equation with the spin- and pseudospin-symmetry for the Coulomb-like potential. Appl. Math. Comput. 216, 911 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Moshinsky M., Szczepanika A.: The Dirac oscillator. J. Phys. A Math. Gen. 22, L817 (1989)

    Article  ADS  Google Scholar 

  12. Kukulin V.I., Loyla G., Moshinsky M.: Dirac equation with an oscillator potential and spin–orbit coupling. Phys. Lett. A 158, 19 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  13. Lisboa R., Malheiro M., de Castro A.S., Alberto P., Fiolhais M.: Pseudospin symmetry and the relativistic harmonic oscillator. Phys. Rev. C 69, 024319 (2004)

    Article  ADS  Google Scholar 

  14. Alberto P., Lisboa R., Malheiro M., de Castro A.S.: Tensor coupling and pseudospin symmetry in nuclei. Phys. Rev. C 71, 034313 (2005)

    Article  ADS  Google Scholar 

  15. Akcay H.: Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. Phys. Lett. A 373, 616 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Akcay H.: The Dirac oscillator with a Coulomb-like tensor potential. J. Phys. A Math. Theor. 40, 6427 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Aydoğdu O., Sever R.: Exact pseudospin symmetric solution of the Dirac equation for pseudoharmonic potential in the presence of tensor potential. Few Body Syst. 47, 193 (2010)

    Article  ADS  Google Scholar 

  18. Aydoğdu O., Sever R.: Pseudospin and spin symmetry in the Dirac equation with Woods–Saxon potential and tensor potential. Eur. Phys. J. A 43, 73 (2010)

    Article  ADS  Google Scholar 

  19. Hamzavi M., Rajabi A.A., Hassanabadi H.: Exact spin and pseudospin symmetry solutions of the Dirac equation for Mie-type potential including a Coulomb-like tensor potential. Few Body Syst. 48, 171 (2010)

    Article  ADS  Google Scholar 

  20. Hamzavi M., Rajabi A.A., Hassanabadi H.: Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method. Phys. Lett. A 374, 4303 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Hamzavi M., Rajabi A.A., Hassanabadi H.: Exactly complete solutions of the Dirac equation with pseudoharmonic potential including linear plus Coulomb-like tensor. Int. J. Mod. Phys. A 26, 1363 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Sun J.X.: Exactly solvable potential with four parameters for diatomic molecules. Acta Phys. Sin. 48, 1992 (1999)

    Google Scholar 

  23. Arda A., Sever R.: Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier. J. Math. Chem. 50, 1920 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Meng J., Sugawara-Tanabe K., Yamaji S., Arima A.: Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line. Phys. Rev. C 59, 154 (1999)

    Article  ADS  Google Scholar 

  25. Meng J., Sugawara-Tanabe K., Yamaji S., Ring P., Arima A.: Pseudospin symmetry in relativistic mean field theory. Phys. Rev. C 58, R628 (1998)

    Article  ADS  Google Scholar 

  26. Ginocchio J.N.: The relativistic foundations of pseudospin symmetry in nuclei. Nucl. Phys. A 654, 663c (1999)

    Article  ADS  Google Scholar 

  27. Ginocchio J.N.: A relativistic symmetry in nuclei. Phys. Rep. 315, 231 (1999)

    Article  ADS  Google Scholar 

  28. Pekeris C.L.: The rotation–vibration coupling in diatomic molecules. Phys. Rev. 45, 98 (1934)

    Article  ADS  Google Scholar 

  29. Ikhdair S.M., Sever R.: Two approximation schemes to the bound states of the Dirac–Hulthén problem. J. Phys. A Math. Theor. 44, 355301 (2011)

    Article  MathSciNet  Google Scholar 

  30. He S., Jia C.-S.: Approximate analytical solutions of the Klein–Gordon equation with the Pöschl–Teller potential including the centrifugal term. Phys. Scr. 81, 045001 (2010)

    Article  ADS  Google Scholar 

  31. Ikhdair S.M.: An approximate κ-state solutions of the Dirac equation for the generalized morse potential under spin and pseudospin-symmetry. J. Math. Phys. 52, 052303 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  32. Ikhdair S.M.: An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A. 39, 307 (2009)

    Article  ADS  Google Scholar 

  33. Nikiforov A.F., Uvarov V.B.: Special Functions of Mathematical Physics. Birkhausr, Berlin (1988)

    Book  MATH  Google Scholar 

  34. Ikhdair S.M.: Vibrational diatomic molecule in the Klein–Gordon equation with hyperbolic scalar and vector potentials. Int. J. Mod. Phys. C 20(10), 1563 (2009)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Majid Hamzavi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hamzavi, M., Ikhdair, S.M. Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction. Few-Body Syst 54, 1741–1752 (2013). https://doi.org/10.1007/s00601-012-0493-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-012-0493-0

Keywords

Navigation