A New Systematical Approach to the Exact Solutions of the Relativistic Dirac Woods Saxon Problem
Using a recently applied systematical method for solving the Dirac equation with spherically symmetric local interaction, we analyzed the problem of a relativistic Dirac particle in the presence of the q-deformed Woods-Saxon potential. The relativistic energy spectrums and two-component spinor wavefunctions, established in terms of the Jacobi polynomials, are obtained analytically. It is shown that the utilizing nonrelativistic limit can be easily and directly reproduced the nonrelativistic Schrödinger Woods-Saxon problem. The method which is labelled by the Nikiforov-Uvarov (NU) is used in the calculations so as to attempt the formalism that is introduced for the first time by A. D. Alhaidari [Int. J. Mod. Phys. A 18, 4955 (2003)]. It is also observed that the energy eigenvalues of the ”new” type Woods-Saxon potential depend on the deformation parameter q. PACS number(s): 03.65.Pm, 03.65.Ge, 02.30.Gp