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Few-Body Systems

, Volume 52, Issue 1–2, pp 19–29 | Cite as

Relativistic Morse Potential and Tensor Interaction

  • M. HamzaviEmail author
  • A. A. Rajabi
  • H. Hassanabadi
Article

Abstract

In this paper, by applying the Pekeris approximation, we present solutions of the Dirac equation for the Morse potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling number κ under spin and pseudospin symmetry limits. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in their closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are given, too.

Keywords

Dirac Equation Morse Potential Spin Symmetry Tensor Interaction Pseudospin Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ginocchio J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414(4–5), 165 (2005)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Bohr A., Hamamoto I., Mottelson B.R.: Pseudospin in rotating nuclear potentials. Phys. Scr. 26, 267 (1982)ADSCrossRefGoogle Scholar
  3. 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)ADSCrossRefGoogle Scholar
  4. 4.
    Troltenier D., Bahri C., Draayer J.P.: Generalized pseudo-SU(3) model and pairing. Nucl. Phys. A 586, 53 (1995)ADSCrossRefGoogle Scholar
  5. 5.
    Page P.R., Goldman T., Ginocchio J.N.: Relativistic symmetry suppresses quark spin-orbit splitting. Phys. Rev. Lett. 86, 204 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    Ginocchio J.N., Leviatan A., Meng J., Zhou S.G.: Test of pseudospin symmetry in deformed nuclei. Phys. Rev. C 69, 034303 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    Ginocchio J.N.: Pseudospin as a relativistic symmetry. Phys. Rev. Lett. 78(3), 436 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    Hecht K.T., Adler A.: Generalized seniority for favored J ≠ 0 pairs in mixed configurations. Nucl. Phys. A 137, 129 (1969)ADSCrossRefGoogle Scholar
  9. 9.
    Arima A., Harvey M., Shimizu K.: Pseudo LS coupling and pseudo SU3 coupling schemes. Phys. Lett. B 30, 517 (1969)ADSCrossRefGoogle Scholar
  10. 10.
    Ikhdair S.M., Sever R.: Approximate bound state solutions of Dirac equationwith Hulthén potential including Coulomb-like tensor potential. Appl. Math. Comput. 216, 911 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Moshinsky M., Szczepanika A.: The Dirac oscillator. J. Phys. A Math. Gen. 22, L817 (1989)ADSCrossRefGoogle Scholar
  12. 12.
    Kukulin V.I., Loyla G., Moshinsky M.: A Dirac equation with an oscillator potential and spin-orbit coupling. Phys. Lett. A 158, 19 (1991)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Lisboa R., Malheiro M., de Castro A.S., Alberto P., Fiolhais M.: Pseudospin symmetry and the relativistic harmonic oscillator. Phys. Rev. C 69, 24319 (2004)ADSCrossRefGoogle Scholar
  14. 14.
    Alberto P., Lisboa R., Malheiro M., de Castro A.S.: Tensor coupling and pseudospin symmetry in nuclei. Phys. Rev. C 71, 034313 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    Akcay H.: Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. Phys. Lett. A 373, 616 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Akcay H.: The Dirac oscillator with a Coulomb-like tensor potential. J. Phys. A Math. Theor. 40, 6427 (2007)MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 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)ADSCrossRefGoogle Scholar
  18. 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)ADSCrossRefGoogle Scholar
  19. 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)ADSCrossRefGoogle Scholar
  20. 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)MathSciNetADSCrossRefGoogle Scholar
  21. 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)MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    Morse P.M.: Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34, 57 (1929)ADSCrossRefGoogle Scholar
  23. 23.
    Berkdemir C.: Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term. Nucl. Phys. A 770, 32 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Berkdemir, C.: Erratum to: “Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term” [Nucl. Phys. A 770 (2006) 32–39]. Nucl. Phys. A 821, 262 (2009)Google Scholar
  25. 25.
    Agboola, D.: Spin symmetry in the relativistic q-deformed Morse potential. Few-Body Syst. doi: 10.1007/s00601-011-0235-8
  26. 26.
    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)ADSCrossRefGoogle Scholar
  27. 27.
    Meng J., Sugawara-Tanabe K., Yamaji S., Ring P., Arima A.: Pseudospin symmetry in relativistic mean field theory. Phys. Rev. C 58, R628 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    Pekeris C.L.: The Rotation-vibration coupling in diatomic molecules. Phys. Rev. 45, 98 (1934)ADSzbMATHCrossRefGoogle Scholar
  29. 29.
    Nikiforov A.F., Uvarov V.B.: Special Functions of Mathematical Physics. Birkhauser, Berlin (1988)zbMATHGoogle Scholar
  30. 30.
    Tezcan C., Sever R.: A general approach for the exact solution of the Schrödinger equation. Int. J. Theor. Phys. 48, 337 (2009)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Physics DepartmentShahrood University of TechnologyShahroodIran

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