Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem

TL;DR

This paper analytically explores how the Hulthen potential influences spin and pseudospin symmetry solutions in the Dirac equation, incorporating orbital dependencies and using the Nikiforov-Uvarov method for various quantum states.

Contribution

It introduces an effective Hulthen-square approximation to include orbital dependencies in solving the Dirac equation with spin and pseudospin symmetry.

Findings

Derived analytical energy eigenvalues for degenerate states.

Presented wave functions for multiple quantum numbers.

Analyzed the impact of the Hulthen potential on symmetry solutions.

Abstract

The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. The spin and pseudospin symmetry along with orbital dependency (pseudospin-orbit and spin-orbit dependent couplings) of the Dirac equation are included to the solution by introducing the Hulthen-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthen potential. The analytical solutions of the Dirac equation for the Hulthen potential with the spin-orbit and pseudospin-orbit-dependent couplings are obtained by using the Nikiforov-Uvarov (NU) method. The energy eigenvalue equations and wave functions for various degenerate states are presented for several spin-orbital, pseudospin-orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry. Keywords: Spin and pseudospin symmetry; orbital dependency; Dirac equation; Hulthen potential; Nikiforov-Uvarov Method.