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

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

2012-03-09

arxiv.org/abs/1203.2023v1

Cent. Eur. J. Phys. 10 (2) (2012) 361-381

Physics

Quantum Physics

21 pages, 6 figures

Scientific paper

10.2478/s11534-011-0121-5

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 {\kappa}. 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 {\alpha}. 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 {\alpha} 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.

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