Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential

We solve the Dirac equation approximately for the attractive scalar S(r)S(r) and repulsive vector V(r)V(r) Hulthén potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number κκ. 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 κκ values under the condition of exact spin symmetry in the presence or absence of tensor coupling.