  Using an approximation scheme to deal with the centrifugal
(pseudo-centrifugal) term, we solve the Dirac equation with the screened
Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number
{\kappa}. Based on the spin and pseudospin symmetry, analytic bound state
energy spectrum formulas and their corresponding upper- and lower-spinor
components of two Dirac particles are obtained using a shortcut of the
Nikiforov-Uvarov method. We find a wide range of permissible values for the
spin symmetry constant C_{s} from the valence energy spectrum of particle and
also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of
antiparticle. Further, we show that the present potential interaction becomes
less (more) attractive for a long (short) range screening parameter {\alpha}.
To remove the degeneracies in energy levels we consider the spin and pseudospin
solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A
few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa,
the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes
zero (Coulomb potential field) and the non-relativistic limit of our solution
are studied. The nonrelativistic solutions are compared with those obtained by
other methods.
