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Approximate Relativistic Bound State Solutions of the Tietz–Hua Rotating Oscillator for Any κ-State

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Abstract

Approximate analytical solutions of the Dirac equation with Tietz–Hua (TH) potential are obtained for arbitrary spin–orbit quantum number κ using the Pekeris approximation scheme to deal with the spin–orbit coupling terms κ(κ ± 1)r −2. In the presence of exact spin and pseudo-spin symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov–Uvarov method. The cases of the Morse potential, the generalized Morse potential and non-relativistic limits are studied.

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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. Commun. 216, 911 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tietz T.: Note concerning the elastic scattering of low-energy electrons in Thomas–Fermi theory. J. Chem. Phys. 38, 3036 (1963)

    Article  ADS  Google Scholar 

  12. Hua W.: Four-parameter exactly solvable potential for diatomic molecules. Phys. Rev. A 24, 2524 (1990)

    Article  ADS  Google Scholar 

  13. Natanson G.A.: Comments on ‘Four-parameter exactly solvable potential for diatomic molecules’. Phys. Rev. A 44, 3377 (1991)

    Article  ADS  Google Scholar 

  14. Levin E., Partridge H., Stallcop J.R.: Collision integrals and high temperature transport properties for N–N, O–O, and N–O. J. Thermophys. Heat Transf. 4, 469 (1990)

    Article  ADS  Google Scholar 

  15. Pack R.T.: On improved WKB (uniform asymptotic) quantum conditions, Dunham corrections, the Langer modification, and RKR potentials. J. Chem. Phys. 57, 4612 (1972)

    Article  ADS  Google Scholar 

  16. Kunc J.A., Gordillo-Vázquez F.J.: Rotational–vibrational levels of diatomic molecules represented by the Tietz–Hua rotating oscillator. J. Phys. Chem. A 101, 1595 (1997)

    Article  Google Scholar 

  17. Morse P.M.: Diatomic molecules according to the wave mechanics II: vibrational levels. Phys. Rev. 34, 57 (1929)

    Article  ADS  MATH  Google Scholar 

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

    MATH  Google Scholar 

  19. Yaşuk F., Berkdemir C., Berkdemir A.: Exact solutions of the Schrödinger equation with non-central potential by the Nikiforov–Uvarov method. J. Phys. A Math. Gen. 38, 6579 (2005)

    Article  ADS  MATH  Google Scholar 

  20. Setare M.R., Haidari S.: Bound states of the Dirac equation with some physical potentials by the Nikiforov–Uvarov method. Phys. Scr. 81, 015201 (2010)

    Article  ADS  Google Scholar 

  21. Ikhdair S.M., Sever R.: Approximate eigenvalue and eigenfunction solutions for the generalized Hulthen potential with any angular momentum. J. Math. Chem. 42, 461 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Miranda M.G., Sun G.H., Dong S.H.: The solution of the second Pösxhl–Teller like potential by Nikiforov–Uvarov method. Int. J. Mod. Phys. E 19, 123 (2010)

    Article  ADS  Google Scholar 

  23. Hamzavi M., Rajabi A.A.: Exact solutions of the Dirac equation with Coulomb plus a novel angle-dependent potential. Z. Naturforsch. 66a, 533 (2011)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Hamzavi M., Hassanabadi H., Rajabi A.A.: Approximate pseudospin solutions of the Dirac equation with the Eckart potential including a Coulomb-like tensor potential. Int. J. Theor. Phys. 50, 454 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Ikhdair S.M., Sever R.: Any l-state solutions of the Woods–Saxon potential in arbitrary dimensions within the new improved quantization rule. Int. J. Mod. Phys. A 25, 3941 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Ikhdair S.M., Abu-Hasna J.: Quantization rule solution to the Hulthén potential in arbitrary dimension with a new approximate scheme for the centrifugal term. Phys. Scr. 83, 025002 (2011)

    Article  ADS  Google Scholar 

  28. Cheng Y.F., Dai T.Q.: Exact solution of the Schrödinger equation for the modified Kratzer potential plus a ring-shaped potential by the Nikiforov–Uvarov method. Phys. Scr. 75, 274 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ikhdair S.M., Sever R.: Exact solution of the Klein–Gordon equation for the PT-symmetric generalized Woods–Saxon potential by the Nikiforov–Uvarov method. Ann. Phys. (Berlin) 16, 218 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Aktaş M., Sever R.: Exact supersymmetric solutions of Schrödinger equation for central confining potentials by using the Nikiforov–Uvarov method. J. Mol. Struct. Theochem 710, 223 (2004)

    Article  Google Scholar 

  31. 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 

  32. Şimşek M., Eğrifes H.: The Klein–Gordon equation of generalized Hulthén potential in complex quantum mechanics. J. Phys. A Math. Gen. 37, 4379 (2004)

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Eğrifes H., Sever R.: Bound-state solutions of the Klein–Gordon equation for the generalized PT-symmetric Hulthén potential. Int. J. Theor. Phys. 46, 935 (2007)

    Article  MATH  Google Scholar 

  35. Ikhdair S.M., Sever R.: Bound states of the Klein–Gordon for exponential-type potentials in D-dimensions. Phys. Scr. 79, 035002 (2009)

    Google Scholar 

  36. Ikhdair S.M.: Bound states of the Klein–Gordon for exponential-type potentials in D-dimensions. J. Quantum Inf. Sci. 1, 73 (2011)

    Article  Google Scholar 

  37. Saad N.: The Klein–Gordon equation with a generalized Hulthén potential in D-dimensions. Phys. Scr. 76, 623 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. 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 

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

    Article  Google Scholar 

  40. 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 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Ikhdair S.M., Sever R.: Approximate analytical solutions of the generalized Woods–Saxon potentials including the spin–orbit coupling term and spin symmetry. Cent. Eur. J. Phys. 8, 665 (2010)

    Article  Google Scholar 

  43. 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 

  44. 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 

  45. 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 

  46. Berkdemir C.: Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term. Nucl. Phys. A 770, 32 (2006)

    Article  ADS  Google Scholar 

  47. Berkdemir C.: Erratum to: Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term. Nucl. Phys. A 821, 262 (2009)

    Article  ADS  Google Scholar 

  48. Aydoğdu O., Sever R.: Pseudospin and spin symmetry in Dirac–Morse problem with a tensor potential. Phys. Lett. B 703, 379 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  49. Ikhdair, S.M., Sever, R.: Exact quantization rule to the Kratzer-type potentials: An application to the diatomic molecules. J. Math. Chem. 45, 1137 (2009)

    Google Scholar 

  50. Greiner W.: Relativistic Quantum Mechanics, Wave Equations, 3rd edn. Springer, Berlin (2000)

    Google Scholar 

  51. 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 

  52. 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 

  53. 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 

  54. Zhou S.G., Meng J., Ring P.: Spin symmetry in the anti-nucleon spectrum. Phys. Rev. Lett. 91, 262501 (2003)

    Article  ADS  Google Scholar 

  55. He X.T., Zhou S.G., Meng J., Zhao E.G., Scheid W.: Test of spin symmetry in anti-nucleon spectra. Euro. Phys. J. A 28, 265 (2006)

    Article  ADS  Google Scholar 

  56. Deng Z.H., Fan Y.P.: A potential function of diatomic molecules. Shandong Univ. J. 7, 162 (1957)

    Google Scholar 

  57. Ikhdair S.M.: Rotational and 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 

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Authors and Affiliations

  1. Physics Department, Near East University, North Cyprus, Mersin 10, Nicosia, 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. Approximate Relativistic Bound State Solutions of the Tietz–Hua Rotating Oscillator for Any κ-State. Few-Body Syst 53, 473–486 (2012). https://doi.org/10.1007/s00601-012-0470-7

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  • DOI: https://doi.org/10.1007/s00601-012-0470-7

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