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formerly Central European Journal of Physics


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Approximate κ-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

1Physics Department, Near East University, Nicosia, North Cyprus, Turkey

© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Physics. Volume 10, Issue 2, Pages 361–381, ISSN (Online) 2391-5471, DOI: 10.2478/s11534-011-0121-5, March 2012

Publication History

Published Online:
2012-03-31

Abstract

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.

Keywords: Dirac equation; Spin symmetry; Pseudospin symmetry; Screened Coulomb potential; Approximation scheme; Nikiforov-Uvarov method

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