Spin symmetry

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Approximate κ-state Solutions to the Dirac-Yukawa Problem Based on the Spin and Pseudospin Symmetry

Journal Title, Volume, Page: 
Central European Journal of Physics , Volume 10, Issue 2, pp 361-381
Year of Publication: 
2012
Authors: 
Sameer M. Ikhdair
Physics Department, Near East University, Nicosia, North Cyprus, Turkey
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Preferred Abstract (Original): 

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.

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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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Solutions of The Spatially-Dependent Mass Dirac Equation with the Spin and Pseudospin Symmetry for the Coulomb-Like Potential

Journal Title, Volume, Page: 
Applied Mathematics and Computation, 216, 545–555
Year of Publication: 
2010
Authors: 
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, North Cyprus, Turkey
Current Affiliation: 
Department of Physics, An-Najah National University, Nablus, Palestine
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original): 

We study the effect of spatially dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3+1)-dimensions for any arbitrary spin-orbit κ state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases (l=l˜=0, i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated.

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