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Relativistic New Yukawa-Like Potential and Tensor Coupling

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Abstract

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number \({\kappa}\) . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, −T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schrödinger solutions for Yukawa and inversely quadratic Yukawa potentials.

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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)

    ADS  Google Scholar 

  10. Ikhdair S.M., Sever R.: Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor 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.: A 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. Akçay 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. Akçay H.: The Dirac oscillator with a Coulomb-like tensor potential. J. Phys. A Math. Theor. 40, 6427 (2007)

    Article  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. 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 

  19. Hamzavi M., Rajabi A.A., Hassanabadi H.: Relativistic Morse potential and tensor interaction. Few-Body Syst. 52, 19 (2012)

    Article  ADS  Google Scholar 

  20. Hamzavi M., Ikhdair S.M., Ita B.I.: Approximate spin and pseudospin solutions to the Dirac equation for the inversely quadraticYukawa potential and tensor interaction. Phys. Scr. 85, 045009 (2012)

    Article  ADS  Google Scholar 

  21. Sever R., Tezcan C., Aktaş M., Yeşiltaş O.: Exact solution of Schrödinger equation for pseudoharmonic potential. J. Math. Chem. 43, 845 (2007)

    Article  Google Scholar 

  22. Ikhdair S.M., Sever R.: Exact polynomial eigensolutions of the Schrödinger equation for the pseudoharmonic potential. J. Mol. Struct. Theochem 806, 155 (2007)

    Article  Google Scholar 

  23. Dong S.H., Gu X.Y., Ma Z.Q., Dong S.: Exact solutions of the Dirac equation with a Coulomb plus scalar potential in 2+1 dimensions. Int. J. Mod. Phys. E 11, 483 (2002)

    Article  ADS  Google Scholar 

  24. McKeon D.G.C., Leeuwen G.V.: The Dirac equation in a pseudoscalar Coulomb potential. Mod. Phys. Lett. A 17, 1961 (2002)

    Article  ADS  MATH  Google Scholar 

  25. Ikhdair S.M., Sever R.: Exact solutions of the radial Schrödinger equation for some physical potentials. Cent. Eur. J. Phys. 5, 516 (2007)

    Article  Google Scholar 

  26. Hamzavi M., Hassanabadi H., Rajabi A.A.: Exact solutions of Dirac equation with Hartmannn potential by Nikiforov–Uvarov method. Int. J. Mod. Phys. E 19, 2189 (2010)

    Article  ADS  Google Scholar 

  27. Hamzavi M., Hassanabadi H., Rajabi A.A.: Exact solution of Dirac equation for Mie-type potential by using the Nikiforov–Uvarov method under the pseudospin and spin symmetry limit. Mod. Phys. Lett. A 25, 2447 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. 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 

  29. Zhang L.H., Li X.P., Jia C.S.: Approximate analytical solutions of the Dirac equation with the generalized Morse potential model in the presence of the spin symmetry and pseudo-spin symmetry. Phys. Scr. 80, 035003 (2009)

    Article  ADS  Google Scholar 

  30. Dong S.H., Lozada-Cassou M.: On the analysis of the eigenvalues of the Dirac equation with a 1/rpotential in D dimensions. Int. J. Mod. Phys. E 13, 917 (2004)

    Article  ADS  Google Scholar 

  31. Ikhdair S.M., Sever R.: Exact bound states of the D-dimensional Klein–Gordon equation with equal scalar and vector ring-shaped pseudoharmonic potentials. Int. J. Mod. Phys. C 19, 1425 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Ikhdair S.M., Sever R.: Effective Schrödinger equation with general ordering ambiguity position-dependent mass Morse potential. Mol. Phys. 110, 1415 (2012)

    Article  ADS  Google Scholar 

  33. Ikhdair S.M., Sever R.: Two approximation schemes to the bound states of the Dirac–Hulthen problem. J. Phys. A Math. Theor. 44, 345301–29 (2011)

    Google Scholar 

  34. Dong S.H.: The realization of dynamic group for the pseudoharmonic oscillator. Appl. Math. Lett. 16, 199 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhang M.C., Huang-Fu G.Q., An B.: Pseudospin symmetry for a new ring-shaped non-spherical harmonic oscillator potential. Phys. Scr. 80, 065018 (2009)

    Article  ADS  Google Scholar 

  36. Wei G.F., Dong S.H.: Pseudospin symmetry in the relativistic Manning–Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term. Phys. Lett. B 686, 288 (2010)

    Article  ADS  Google Scholar 

  37. Ikhdair S.M.: On the bound-state solutions of the Manning–Rosen potential including an improved approximation to the orbital centrifugal term. Phys. Scr. 83, 015010 (2011)

    Article  ADS  Google Scholar 

  38. Oyewumi K.J., Akinpelu F.O., Agboola A.D.: Exactly complete solutions of the pseudoharmonic potential in N-dimensions. Int. J. Theor. Phys. 47, 1039 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  39. Ikhdair S.M., Sever R.: Approximate bound states of the Dirac equation with some physical quantum potentials. Appl. Math. Comput. 218, 10082 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  40. Ikhdair S.M.: Approximate \({\kappa}\) -state solutions to the Dirac–Yukawa problem based on the spin and pseudospin symmetry. Cent. Eur. J. Phys. 10, 361 (2012)

    Article  Google Scholar 

  41. Taseli H.: Int. J. Quant. Chem. 63, 949 (1997)

    Article  Google Scholar 

  42. Kermode M.W., Allen M.L.J., Mctavish J.P., Kervell A.: J. Phys. G Nucl. Part. Phys. 10, 773 (1984)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. Greene R.L., Aldrich C.: Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14, 2363 (1976)

    Article  ADS  Google Scholar 

  46. Aydoğdu O., Sever R.: The Dirac–Yukawa problem in view of pseudospin symmetry. Phys. Scr. 84, 025005 (2011)

    Article  ADS  Google Scholar 

  47. Setare M.R., Haidari S.: Spin symmetry of the Dirac equation with the Yukawa potential. Phys. Scr. 81, 065201 (2010)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  49. Ikhdair S.M.: Rotational and vibrational diatomic molecules in the Klein–Gordon equation with hyperbolic scalar and vector potentials. Int. J. Mod. Phys. C 20, 1563 (2009)

    Article  ADS  MATH  Google Scholar 

  50. Tezcan C., Sever R.: A general approach for the exact solution of the Schrödinger equation. Int. J. Theor. Phys. 48, 337 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  51. Ikhdair S.M.: Exact Klein–Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials. Eur. Phys. J. A 40, 143 (2009)

    Article  ADS  Google Scholar 

  52. Ikhdair S.M.: An approximate \({\kappa}\) -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 

  53. Ikhdair S.M., Sever R.: Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov–Uvarov method. J. Math. Phys. 52, 122108 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  54. Ikhdair S.M.: Approximate solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term. J. Math. Phys. 51, 023525 (2010)

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Physics Department, Near East University, 922022, Nicosia, North Cyprus, Mersin 10, Turkey

    Sameer M. Ikhdair

  2. Department of Basic Sciences, Shahrood Branch Islamic Azad University, Shahrood, Iran

    Majid Hamzavi

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  1. Sameer M. Ikhdair
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  2. Majid Hamzavi
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Correspondence to Majid Hamzavi.

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Ikhdair, S.M., Hamzavi, M. Relativistic New Yukawa-Like Potential and Tensor Coupling. Few-Body Syst 53, 487–498 (2012). https://doi.org/10.1007/s00601-012-0475-2

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