Pseudospin symmetric solutions of the Dirac equation with the modified Rosen–Morse potential using Nikiforov–Uvarov method and supersymmetric quantum mechanics approach

Abstract

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term, we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen–Morse potential including the spin–orbit coupling term by using the Nikiforov–Uvarov method and supersymmetric quantum mechanics approach. The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin–orbit coupling quantum number k are presented under the condition of pseudospin symmetry. The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations. The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.