Z. Naturforsch. **68a,** 279 – 290
(2013)

doi:10.5560/ZNA.2012-0109

Approximate Relativistic Solutions for a New Ring-Shaped Hulthén Potential

Sameer M.
Ikhdair^{1,2} and
Majid
Hamzavi^{3}

^{1 }Physics Department, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine

^{2 }Physics Department, Near East University, 922022 Nicosia, Northern Cyprus, Turkey

^{3 }Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran

Received July 1, 2012/ revised October 8, 2012 / published online February 6, 2013

Approximate bound state solutions of the Dirac equation with the Hulthén plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary *l*-state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthén potential parameters to deal with the strong singular centrifugal potential term *l*(*l* + 1)*r*^{−2}. Under the limiting case, the solution can be easily reduced to the solution of the Schrödinger equation with a new ring-shaped Hulthén potential.

*Key words:* Dirac Equation; Hulthén Potential; Ring-Shaped Potentials; Approximation Schemes; NU Method.

*PACS numbers:* 03.65.Ge; 03.65.Fd; 0.65.Pm; 02.30.Gp