An-Najah Staff

The role of the Hulthén potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar and repulsive vector potentials. The spin and pseudospin symmetry along with orbital dependency (pseudospin–orbit and spin–orbit dependent couplings) of the Dirac equation are included to the solution by introducing the Hulthén-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthén potential. The analytical solutions of the Dirac equation for the Hulthén potential with the spin–orbit and pseudospin–orbit-dependent couplings are obtained by using the Nikiforov–Uvarov (NU) method. The energy eigenvalue equations and wave functions for various degenerate states are presented for several spin–orbital, pseudospin–orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry.

The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthén potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov–Uvarov method is used in the calculations. The orbital dependence (spin–orbit- and pseudospin–orbit-dependent coupling too singular 1/r2) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.