An-Najah Staff

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 approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen–Morse potentials including the spin–orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov–Uvarov (NU) method in closed form. The special cases of the s-wave Dirac equation and the non-relativistic limit of Dirac equation are briefly studied.

 Approximate analytical solutions of the Dirac equation for Tietz-Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin-orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms κ (κ±1)r^-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

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.