Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Creative Commons License

Ikhdair S. M., Sever R.

Central European Journal of Physics, vol.8, no.4, pp.652-666, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.2478/s11534-009-0118-5
  • Journal Name: Central European Journal of Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.652-666
  • Keywords: Dirac equation, Nikiforov-Uvarov method, Pseudospin symmetry, Spin symmetry, Woods-Saxon potential
  • Middle East Technical University Affiliated: Yes

Abstract

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others. © 2009 Versita Warsaw and Springer-Verlag Berlin Heidelberg.