Advertisement

The European Physical Journal A

, Volume 43, Issue 2, pp 185–190 | Cite as

A novel algebraic approach to spin symmetry for Dirac equation with scalar and vector second Pöschl-Teller potentials

  • Gao-Feng Wei
  • Shi-Hai Dong
Regular Article - Theoretical Physics

Abstract

By a novel algebraic method we study the approximate solution to the Dirac equation with scalar and vector second Pöschl-Teller potential carrying spin symmetry. The transcendental energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. It is found that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter \( \alpha\) goes to zero. The equally scalar and vector case is studied briefly.

Keywords

Dirac Equation Riccati Equation Energy Eigenvalue Algebraic Approach Spin 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Arima, M. Harvey, K. Shimizu, Phys. Lett. B 30, 517 (1969)CrossRefADSGoogle Scholar
  2. 2.
    K.T. Hecht, A. Adeler, Nucl. Phys. A 137, 129 (1969)CrossRefADSGoogle Scholar
  3. 3.
    A. Bohr, I. Hamamoto, B.R. Mottelson, Phys. Scr. 26, 267 (1982)CrossRefADSGoogle Scholar
  4. 4.
    J. Dudek, W. Nazarewicz, Z. Szymanski, G.A. Leander, Phys. Rev. Lett. 59, 1405 (1987)CrossRefADSGoogle Scholar
  5. 5.
    D. Troltenier, C. Bahri, J.P. Draayer, Nucl. Phys. A 586, 53 (1995)CrossRefADSGoogle Scholar
  6. 6.
    J.N. Ginocchio, Phys. Rev. Lett. 95, 252501 (2005)CrossRefADSGoogle Scholar
  7. 7.
    J.N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997)CrossRefADSGoogle Scholar
  8. 8.
    S.G. Zhou, J. Meng, P. Ring, Phys. Rev. Lett. 91, 262501 (2003)CrossRefADSGoogle Scholar
  9. 9.
    J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, A. Arima, Phys. Rev. C 58, R628 (1998)CrossRefADSGoogle Scholar
  10. 10.
    R. Lisboa, M. Malheiro, A.S. De Castro, P. Alberto, M. Fiolhais, Phys. Rev. C 69, 024319 (2004)CrossRefADSGoogle Scholar
  11. 11.
    A.S. De Castro, P. Alberto, R. Lisboa, M. Malheiro, Phys. Rev. C 73, 054309 (2006)CrossRefADSGoogle Scholar
  12. 12.
    J.Y. Guo, Z.Q. Sheng, Phys. Lett. A 338, 90 (2005)zbMATHCrossRefMathSciNetADSGoogle Scholar
  13. 13.
    C. Berkdemir, Nucl. Phys. A 770, 32 (2006)CrossRefADSGoogle Scholar
  14. 14.
    W.C. Qiang, R.S. Zhou, Y. Gao, J. Phys. A: Math. Theor. 40, 1677 (2007)zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    O. Bayrak, I. Boztosun, J. Phys. A: Math. Theor. 40, 11119 (2007)zbMATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    A. Soylu, O. Bayrak, I. Boztosun, J. Phys. A: Math. Theor. 41, 065308 (2008)CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    C.S. Jia, P. Guo, X.L. Peng, J. Phys. A: Math. Theor. 39, 7737 (2006)zbMATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    L.H. Zhang, X.P. Li, C.S. Jia, Phys. Lett. A 372, 2201 (2008)CrossRefMathSciNetADSGoogle Scholar
  19. 19.
    Y. Xu, H. Su, C.S. Jia, J. Phys. A: Math. Theor. 41, 255302 (2008)CrossRefADSGoogle Scholar
  20. 20.
    G.F. Wei, S.H. Dong, Phys. Lett. A 373, 49 (2008)CrossRefMathSciNetADSGoogle Scholar
  21. 21.
    A.D. Alhaidari, H. Bahlouli, A. Al-Hasan, Phys. Lett. A 349, 87 (2006)CrossRefMathSciNetADSGoogle Scholar
  22. 22.
    I. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951)zbMATHCrossRefMathSciNetADSGoogle Scholar
  23. 23.
    O. Bayrak, G. Kocak, I. Boztosun, J. Phys. A: Math. Theor. 39, 11521 (2006)zbMATHCrossRefMathSciNetADSGoogle Scholar
  24. 24.
    R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976)CrossRefADSGoogle Scholar
  25. 25.
    C.N. Yang, in Monopoles in Quantum Field Theory, Proceedings of the Monopole Meeting, Trieste, Italy, edited by N.S. Craigie, P. Goddard, W. Nahm (World Scientific, Singapore, 1982) p. 237Google Scholar
  26. 26.
    F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)CrossRefMathSciNetGoogle Scholar
  27. 27.
    J.W. Dabrowska, A. Khare, U.P. Sukhatme, J. Phys. A: Math. Gen. 21, L195 (1988)CrossRefMathSciNetADSGoogle Scholar
  28. 28.
    I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series, and Products, fifth edition (Academic Press, New York, 1994)Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of PhysicsXi’an University of Arts and ScienceXi’anPRC
  2. 2.Escuela Superior de Fısica y MatemáticasInstituto Politécnico NacionalMexico D. F.Mexico

Personalised recommendations