Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries

Abstract: By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector P\"oschl-Teller (PT) potentials with arbitrary spin-orbit -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 the hypergeometric functions are obtained by means of the wave function analysis. The spin- Dirac equation and the spin- Klein-Gordon (KG) equation with the complex P\"oschl-Teller potentials share the same energy spectrum under the choice of (i.e., exact spin and p-spin symmetries).