A B C
Z. Naturforsch. 69a, 111 – 121 (2014)
doi:10.5560/ZNA.2013-0081
Laplace Transformation Approach to the Spin Symmetry of the Mie-Type Potential with a Coulomb Tensor Interaction
Mahdi Eshghi1 and Sameer M. Ikhdair2,3
1 Department of Physics, Imam Hossein Comprehensive University, Tehran, Iran
2 Department of Physics, Faculty of Science, an-Najah National University, Nablus, West Bank, Palestine
3 Department of Electrical and Electronic Engineering, Near East University, 922022 Nicosia, Northern Cyprus, Mersin 10, Turkey
Received April 2, 2013 / revised September 27, 2013 / published online January 22, 2014
Reprint requests to: M. E.; E-mail: eshgi54@gmail.com, kpeshghi@ihu.ac.ir
The Dirac equation is solved exactly under the condition of spin symmetry for a spin 1/2 particle in the field of Mie-type potential and a Coulomb-like tensor interaction via the Laplace transform approach (LTA). The Dirac bound state energy equation and the corresponding normalized wave functions are obtained in closed forms with any spin-orbit coupling term κ. The effects of the tensor interaction and the potential parameters on the bound states are also studied. It is noticed that the tensor interaction removes degeneracy between two states in spin doublets. Some numerical results are given and a few special cases of interest are presented. We have demonstrated that in the nonrelativistic limit, the solutions of the Dirac system converges to that of the Schrödinger system. The nonrelativistic limits of the present solutions are compared with the ones obtained by findings of other methods. Our results are sufficiently accurate for practical purpose.
Key words: Dirac Equation; Schrödinger Equation; Mie-Type Potential; Laplace Transformation Approach; Tensor Interaction.
PACS numbers: 03.65.Pm; 03.65.Ge; 02.30.Gp
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