Applying an appropriate approximation scheme to deal with the centrifugal term, pseudospin and spin symmetric solutions of the Dirac–Yukawa problem with tensor interaction are investigated based on supersymmetric quantum mechanics (SUSYQM) and shape invariance (SI) formalism. We show that the energy eigenvalues equation is simply obtained by using the methodology of SUSYQM and SI. The corresponding wave functions are obtained in terms of hypergeometric functions. Effects of tensor interaction on the bound states and eigenfunctions are also investigated numerically. Further, we compare our results with those given in the literature, which are obtained by using the Nikiforov–Uvarov and asymptotic iteration methods.
Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper-and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper-and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.
Based on the significant role of spin and pseudospin symmetries in hadron and nuclear spectroscopy, we have investigated Dirac equation under scalar and vector potentials of cotangent hyperbolic form besides a Coulomb tensor interaction via an approximate analytical scheme. The considered potential for small potential parameter resembles the well-established Kratzer potential. In addition, we see how the tensor term removes the degeneracy of doublets. After an acceptable approximation, namely a Pekeris-type one, we see that the problem is simply solved via the quantum mechanical idea of supersymmetry without having to deal with the cumbersome, complicated and time-consuming numerical programming.
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