Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem

Berkdemir, Cuneyt
Sever, Ramazan
The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S((r) over right arrow) and repulsive vector V((r) over right arrow) potentials. The spin and pseudospin symmetry along with orbital dependency (pseudospin-orbit and spin-orbit dependent couplings) of the Dirac equation are included to the solution by introducing the Hulthen-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthen potential. The analytical solutions of the Dirac equation for the Hulthen potential with the spin-orbit and pseudospin-orbit-dependent couplings are obtained by using the Nikiforov-Uvarov (NU) method. The energy eigenvalue equations and wave functions for various degenerate states are presented for several spin-orbital, pseudospin-orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry.


MUSTAFA, O; Sever, Ramazan (1991-10-01)
The shifted 1/N expansion method has been extended to solve the Klein-Gordon equation with both scalar and vector potentials. The calculations are carried out to the third-order correction in the energy series. The analytical results are applied to a linear scalar potential to obtain the relativistic energy eigenvalues. Our numerical results are compared with those obtained by Gunion and Li [Phys. Rev. D 12, 3583 (1975)].
Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (2010-02-01)
The Dirac equation is solved for some exponential potentials the hypergeometric-type potential, the generalized Morse potential, and the Poschl-Teller potential with any spin-orbit quantum number kappa in the case of spin and pseudospin symmetry. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations and the corresponding wave functions are obtained by using a generalization of the Nikiforov-Uvarov method.
Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential
IKHDAİR, SAMEER; Sever, Ramazan (2010-03-15)
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 kappa 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 exa...
Approximate eigenvalue and eigenfunction solutions for the generalized Hulthen potential with any angular momentum
Ikhdair, Sameer M.; Sever, Ramazan (2007-10-01)
An approximate solution of the Schrodinger equation for the generalized Hulthen potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. We have considered the time-independent Schrodinger equation with the associated form of Hulthen potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthen pot...
Scattering and bound state solutions of the asymmetric Hulthen potential
Arda, Altug; AYDOĞDU, OKTAY; Sever, Ramazan (IOP Publishing, 2011-08-01)
The one-dimensional time-independent Schrodinger equation is solved for the asymmetric Hulthen potential. The reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is observed that the unitary condition is satisfied in the non-relativistic region.
Citation Formats
S. IKHDAİR, C. Berkdemir, and R. Sever, “Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem,” APPLIED MATHEMATICS AND COMPUTATION, pp. 9019–9032, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62791.