A peer-reviewed journal published by K. N. Toosi University of Technology

Document Type : Research Article


1 Depatment of Physics, Imam Hossein Comprehensive University

2 Department of Medical Engineering, Faculty of Health and Medical Engineering, Tehran Medical Sciences, Islamic Azad University, Tehran, Iran

3 Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine


The scattering problems, in the presence of an external potential field, have become highly interesting topics in relativistic and non-relativistic quantum mechanics. It is well known that the scattering of a relativistic particle in the field of a potential can be treated exactly by finding the continuum solutions of the Dirac equation. In this research, we obtain the exact solution to the Dirac equation with the Pöschl-Teller double ring-shaped Coulomb (PTDRSC) potential for any spin-orbit quantum number k. The relativistic scattering amplitude for spin 1/2 particles in the field of this potential has been studied. The wave functions are being expressed in terms of the hyper-geometric series of the continuous states on the k/2π scale. In addition, a formula for the phase shifts has also been found. In the nonrelativistic limits, our solution to the Dirac particle converges to that of the Schrödinger one. At the high temperature, the partition function is being calculated in order to study the behavior of some thermodynamic properties.


• The continuous energy states have been obtained for the radial part of the Dirac equation.
• The relativistic scattering amplitude have calculated for spin 1/2 particles.
• The Pöschl-Teller double ring-shaped Coulomb potential have been used for solution of the relativistic equation.


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