Approximate Dirac solutions of a complex parity-time-symmetric Poschl-Teller potential in view of spin and pseudospin symmetries

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for a spin-1/2 particle subjected to complex parity-time-symmetric scalar and vector Poschl-Teller (PT) potentials with arbitrary spin-orbit kappa-wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of hypergeometric functions are obtained by means of wave function analysis. The spin-kappa Dirac equation and the spin-0 Klein-Gordon equation with complex PT potentials share the same energy spectrum under the choice of S(r) = +/- V(r) (i.e. exact spin and p-spin symmetries).