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Two approximation schemes to the bound states of the Dirac-Hulthén problem. (English) Zbl 1227.81160
Summary: The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthén potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations. The orbital dependence (spin-orbit- and pseudospin-orbit-dependent coupling too singular $1/{r}^{2}$) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular $1/r$ orbital term in the Dirac equation for a wider energy spectrum. Nonrelativistic limits are also obtained on the mapping of the parameters.
##### MSC:
 81Q05 Closed and approximate solutions to quantum-mechanical equations 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 34C14 Symmetries, invariants (ODE) 81Q60 Supersymmetry and quantum mechanics 81R05 Representations of finite-dimensional groups and algebras in quantum theory 34L40 Particular ordinary differential operators 81V35 Applications of quantum theory to nuclear physics