02.30.Gp

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Approximate Solutions to a Spatially-Dependent Mass Dirac Equation for Modified Hylleraas Plus Eckart Potential with Yukawa Potential as a Tensor

Journal Title, Volume, Page: 
Indian Journal of Physics, Volume 88, Issue 7, pp 695-707
Year of Publication: 
2014
Authors: 
Sameer M. Ikhdair
Department of Physics, Faculty of Science, An-Najah National University, New Campus, Nablus, Palestine
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, New campus, Nablus, Palestine
Majid Hamzavi
Department of Physics, University of Zanjan, Zanjan, Iran
Preferred Abstract (Original): 

In presence of spin (pseudo-spin) symmetry, approximate bounded fermionic (anti-fermionic) states of the effective mass Dirac equation for modified Hylleraas plus Eckart potential within Yukawa tensor interaction have been studied by means of the parametric Nikiforov–Uvarov method. We have obtained the analytical relativistic energy eigenvalues and their corresponding normalized two-spinor components of the wave functions in closed form by making an appropriate approximation to centrifugal (pseudo-centrifugal) term for any spin–orbit quantum number κ. Some special cases for various potential models have been investigated in relativistic and nonrelativistic limit. Further, numerical results for energy eigenvalues have been obtained within the exact spin and pseudo-spin symmetries.

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Approximate Eigensolutions of Dirac Equation for the Superposition Hellmann Potential Under Spin and ‎Pseudospin Symmetries

Journal Title, Volume, Page: 
Pramana , Volume 83, Issue 1, pp 49-61
Year of Publication: 
2014
Authors: 
S M IKHDAIR
Department of Physics, Faculty of Science, An- Najah National University, New Campus, Nablus, Palestine
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, New campus, P. O. Box 7, Nablus, Palestine
M HAMZAVI
Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran
Preferred Abstract (Original): 

The Hellmann potential is simply a superposition of an attractive Coulomb potential −a/r plus a Yukawa potential be−δ r /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.

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Approximate Analytical Solutions of the Generalized Woods-Saxon Potentials Including the Spin-Orbit Coupling Term and Spin Symmetry

Journal Title, Volume, Page: 
Cent. Eur. J. Phys., 8(4), 652-666
Year of Publication: 
2010
Authors: 
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia,Cyprus, Turkey
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Ramazan Sever
Department of Physics, Middle East Technical University, 06800, Ankara, Turkey
Preferred Abstract (Original): 

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.

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