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Relativistic Energies and Scattering Phase Shifts for the Fermionic Particles Scattered by Hyperbolical Potential with the Pseudo(spin) Symmetry

In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. By applying an improved Greene-Aldrich approximation scheme within the formalism of functional analytical method, we obtained the spin-orbit quantum numbers dependent scattering phase shifts for the spin and pseudospin symmetries. The normalization constants, lower and upper radial spinor for the two symmetries, and the relativistic energy spectra were presented. Our results reveal that both the symmetry constants ( and ) and the spin-orbit quantum number affect scattering phase shifts significantly.