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Few-Body Systems

, Volume 48, Issue 2–4, pp 171–182 | Cite as

Exact Spin and Pseudospin Symmetry Solutions of the Dirac Equation for Mie-Type Potential Including a Coulomb-like Tensor Potential

  • M. Hamzavi
  • A. A. Rajabi
  • H. Hassanabadi
Article

Abstract

We solve the Dirac equation for Mie-type potential including a Coulomb-like tensor potential under spin and pseudospin symmetry limits with arbitrary spin–orbit coupling quantum number κ. The Nikiforov–Uvarov method is used to obtain analytical solutions of the Dirac equation. Since it is only the wave functions which are obtained in a closed exact form; as for the eigenvalues, only the eigenvalue equations have been given and they have been solved numerically. It is also shown that the degeneracy between spin doublets and pseudospin doublets is removed by tensor interaction.

Keywords

Dirac Equation Spin Symmetry Tensor Interaction Pseudospin Symmetry Tensor Potential 
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.
    Mesa A.D.S., Quesne C., Smirnov Y.F.: Generalized Morse potential: symmetry and satellite potentials. J. Phys. A: Math. Gen. 31, 321 (1998)zbMATHCrossRefADSGoogle Scholar
  2. 2.
    Codriansky S., Cordero P., Salamo S.: On the generalized Morse potential. J. Phys. A: Math. Gen. 32, 6287 (1999)zbMATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Jia C.S., Zeng L.X., Sun L.T.: PT symmetry and shape invariance for a potential well with a barrier. Phys. Lett. A 294, 185 (2002)zbMATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Rong Z., Kjaergaard H.G., Sage M.L.: Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules. Mol. Phys. 101, 2285 (2003)CrossRefADSGoogle Scholar
  5. 5.
    Dong S.H.: The realization of dynamic group for the pseudoharmonic oscillator. Appl. Math. Lett. 16, 199 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jia C.S., Li Y., Sun Y., Liu J.Y., Sun L.T.: Bound states of the five-parameter exponential-type potential model. Phys. Lett. A 311, 115 (2003)zbMATHCrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Haouat S., Chetouani L.: Approximate solutions of Klein–Gordon and Dirac equations in the presence of the Hulthén potential. Phys. Scr. 77, 025005 (2008)CrossRefADSGoogle Scholar
  8. 8.
    Wei G.F., Liu X.Y.: The relativistic bound states of the hyperbolical potential with the centrifugal term. Phys. Scr. 78, 065009 (2008)CrossRefADSGoogle Scholar
  9. 9.
    Zhang L.H., Li X.P., Jia C.S.: Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin–orbit coupling term. Phys. Lett. A 372, 2201 (2008)CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Xu Y., He S., Jia C.S.: Approximate analytical solutions of the Dirac equation with the Pöschl–Teller potential including the spin–orbit coupling term. J. Phys. A: Math. Theor. 41, 255302 (2008)CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Dong S.H., Gu X.Y.: Arbitrary l state solutions of the Schrödinger equation with the Deng-Fan molecular potential. J. Phys.: Conf. Ser. 96, 012109 (2008)CrossRefADSGoogle Scholar
  12. 12.
    Soylu A., Bayrak O., Boztosun I.: κ state solutions of the Dirac equation for the Eckart potential with pseudospin and spin symmetry. J. Phys. A: Math. Theor. 41, 065308 (2008)CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Chen T., Diao Y.F., Jia C.S.: Bound state solutions of the Klein–Gordon equation with the generalized Pöschl–Teller potential. Phys. Scr. 79, 065014 (2009)CrossRefADSGoogle Scholar
  14. 14.
    Chen T., Liu J.Y., Jia C.S.: Approximate analytical solutions of the Dirac–Manning–Rosen problem with the spin symmetry and pseudo-spin symmetry. Phys. Scr. 79, 055002 (2009)CrossRefADSGoogle Scholar
  15. 15.
    Jia C.S., Chen T., Cui L.G.: Approximate analytical solutions of the Dirac equation with the generalized Pöschl–Teller potential including the pseudo-centrifugal term. Phys. Lett. A 373, 1621 (2009)CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Xu Y., He S., Jia C.S.: Reply to ‘comment on’ approximate analytical solutions of the Dirac equation with the Pöschl–Teller potential including spin–orbit coupling. J. Phys. A: Math. Theor. 42, 198002 (2009)CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Taskin F.: Approximate solutions of the Dirac equation for the Manning-Rosen potential including the Spin-Orbit coupling term. Int. J. Theor. Phys. 48, 1142 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Liu X.Y., Wei G.F., Long C.Y.: Arbitrary wave relativistic bound state solutions for the Eckart potential. Int. J. Theor. Phys. 48, 463 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Bohr A., Hamamoto I., Mottelson B.R.: Pseudospin in rotating nuclear potentials. Phys. Scr. 26, 267 (1982)CrossRefADSGoogle Scholar
  20. 20.
    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)CrossRefADSGoogle Scholar
  21. 21.
    Troltenier D., Bahri C., Draayer J.P.: Generalized pseudo-SU(3) model and pairing. Nucl. Phys. A 586, 53 (1995)CrossRefADSGoogle Scholar
  22. 22.
    Page P.R., Goldman T., Ginocchio J.N.: Relativistic symmetry suppresses Quark spin-orbit splitting. Phys. Rev. Lett. 86, 204 (2001)CrossRefADSGoogle Scholar
  23. 23.
    Ginocchio J.N., Leviatan A., Meng J., Zhou S.G.: Test of pseudospin symmetry in deformed nuclei. Phys. Rev. C 69, 034303 (2004)CrossRefADSGoogle Scholar
  24. 24.
    Ginocchio J.N.: Pseudospin as a relativistic symmetry. Phys. Rev. Lett. 78(3), 436 (1997)CrossRefADSGoogle Scholar
  25. 25.
    Ginocchio J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414(4-5), 165 (2005)CrossRefMathSciNetADSGoogle Scholar
  26. 26.
    Hect K.T., Adler A.: Generalized seniority for favored J ≠  0 pairs in mixed configurations. Nucl. Phys. A 137, 129 (1969)CrossRefADSGoogle Scholar
  27. 27.
    Arima A., Harvey M., Shimizu K.: Pseudo LS coupling and pseudo SU3 coupling schemes. Phys. Lett. B 30, 517 (1969)CrossRefADSGoogle Scholar
  28. 28.
    Ikhdair S.M., Sever R.: Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential. Appl. Math. Com. 216, 911 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Moshinsky M., Szczepanika A.: The Dirac oscillator. J. Phys. A: Math. Gen. 22, L817 (1989)CrossRefADSGoogle Scholar
  30. 30.
    Kukulin V.I., Loyla G., Moshinsky M.: A Dirac equation with an oscillator potential and spin-orbit coupling. Phys. Lett. A 158, 19 (1991)CrossRefMathSciNetADSGoogle Scholar
  31. 31.
    Akcay H.: Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential. Phys. Lett. A 373, 616 (2009)CrossRefMathSciNetADSGoogle Scholar
  32. 32.
    Akcay H.: The Dirac oscillator with a Coulomb-like tensor potential. J. Phys. A: Math. Theor. 40, 6427 (2007)zbMATHCrossRefMathSciNetADSGoogle Scholar
  33. 33.
    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)CrossRefADSGoogle Scholar
  34. 34.
    Berkdemir C.: Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term. Nucl. Phys. A 770, 32 (2006)CrossRefADSGoogle Scholar
  35. 35.
    Chen T.S., Lü H.F., Meng J., Zhang S.Q., Zhou S.G.: Pseudospin symmetry in relativistic framework with harmonic oscillator potential and Woods-Saxon potential. Chin. Phys. Lett. 20, 358 (2003)CrossRefADSGoogle Scholar
  36. 36.
    Alhaidari A.D., Bahlouli H., Al-Hasan A.: Dirac and Klein–Gordon equations with equal scalar and vector potentials. Phys. Lett. A. 349, 87 (2006)zbMATHCrossRefMathSciNetADSGoogle Scholar
  37. 37.
    Guo J.Y., Zhou F., Guo F.L., Zhou J.H.: Exact solution of the continuous states for generalized asymmetrical Hartmann potentials under the condition of pseudospin symmetry. Int. J. Mod. Phys. A 22, 4825 (2007)zbMATHCrossRefMathSciNetADSGoogle Scholar
  38. 38.
    Guo J.Y., Sheng Z.Q.: Solution of the Dirac equation for the Woods–Saxon potential with spin and pseudospin symmetry. Phys. Lett. A 338, 90 (2005)zbMATHCrossRefMathSciNetADSGoogle Scholar
  39. 39.
    Qiang W.C., Zhou R.S., Gao Y.: Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry. J. Phys. A: Math. Theor. 40, 1677 (2007)zbMATHCrossRefMathSciNetADSGoogle Scholar
  40. 40.
    Xu Q., Zhu S.J.: Pseudospin symmetry and spin symmetry in the relativistic Woods–Saxon. Nucl. Phys. A 768, 161 (2006)CrossRefADSGoogle Scholar
  41. 41.
    Aydoğdu O., Sever R.: Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit. Ann. Phys. 325, 373 (2010)zbMATHCrossRefADSGoogle Scholar
  42. 42.
    Ikhdair S.M., Sever R.: Approximate eigenvalue and eigenfunction solutions for the generalized Hulthén Potential with any angular momentum. J. Math. Chem. 42, 461 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Erkoc S., Sever R.: Path-integral solution for a Mie-type potential. Phys. Rev. D 30, 2117 (1984)CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    Morse P.M.: Diatomic molecules according to the wave Mechanics. II. Vibrational levels. Phys. Rev. 34, 57 (1929)CrossRefADSGoogle Scholar
  45. 45.
    Ikhdair S.M., Sever R.: On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz. Cent. Eur. J. Phys. 6, 697 (2008)CrossRefGoogle Scholar
  46. 46.
    Ikhdair S.M., Sever R.: Polynomial solutions of the Mie-type potential in the D-dimensional Schrödinger equation. J. Mol. Struc. (Theochem) 13, 855 (2008)Google Scholar
  47. 47.
    Berkdemir C., Berkdemir A., Han J.: Bound state solutions of the Schrödinger equation for modified Kratzer’s molecular potential. Chem. Phys. Lett 417, 326 (2006)CrossRefADSGoogle Scholar
  48. 48.
    Bjorken J.D., Drell S.D.: “Relativistic Quantum Mechanics”. McGraw-Hill, NY (1964)Google Scholar
  49. 49.
    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)CrossRefADSGoogle Scholar
  50. 50.
    Meng J. et al.: Pseudospin symmetry in relativistic mean field theory. Phys. Rev. C 58, R628 (1998)CrossRefADSGoogle Scholar
  51. 51.
    Satchler G.R.: “Direct Nuclear Reactions”. Oxford University Press, London (1983)Google Scholar
  52. 52.
    Nikiforov A.F., Uvarov V.B.: “Special Functions of Mathematical Physics”. Birkhausr, Berlin (1988)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Physics DepartmentShahrood University of TechnologyShahroodIran

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