A novel algebraic approach to spin symmetry for Dirac equation with scalar and vector second Pöschl-Teller potentials

By a novel algebraic method we study the approximate solution to the Dirac equation with scalar and vector second Pöschl-Teller potential carrying spin symmetry. The transcendental energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. It is found that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter $ \alpha$ goes to zero. The equally scalar and vector case is studied briefly