Exact solutions of the Manning-Rosen potential plus a ring-shaped like potential for the Dirac equation: spin and pseudospin symmetry

The analytical bound state solutions of the Dirac equation for the Manning-Rosen potential plus a ring-shaped like potential in spin and pseudospin symmetries are investigated by a proper approximation to the centrifugal term. Using the Nikiforov-Uvarov method, an explicit form of the energy eigenvalue and the corresponding energy eigenstates, expressed in terms of the Jacobi polynomials, are derived. The normalization coefficients of wave functions for spin and pseudospin symmetry solutions are found explicitly.