An-Najah Staff

Approximate bound state solutions of the Dirac equation with the Hulth\'en plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulth\'en potential.

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.

We solve the Dirac equation approximately for the attractive scalar S(r) and repulsive vector V(r) Hulthén potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudospin symmetric concept, we obtain the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov–Uvarov method in closed form. The limit of zero tensor coupling and the non-relativistic solution are obtained. The energy spectrum for various levels is presented for several κ values under the condition of exact spin symmetry in the presence or absence of tensor coupling.

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.