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Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem

Berkdemir, Cuneyt
Sever, Ramazan
The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S((r) over right arrow) and repulsive vector V((r) over right arrow) 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 Hulthen-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthen potential. The analytical solutions of the Dirac equation for the Hulthen 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.