Pseudospin symmetry and its applications

Aydoğdu, Oktay
The pseudospin symmetry concept is investigated by solving the Dirac equation for the exactly solvable potentials such as pseudoharmonic potential, Mie-type potential, Woods-Saxon potential and Hulthén plus ring-shaped potential with any spin-orbit coupling term $\kappa$. Nikiforov-Uvarov Method, Asymptotic Iteration Method and functional analysis method are used in the calculations. The energy eigenvalue equations of the Dirac particles are found and the corresponding radial wave functions are presented in terms of special functions. We look for the contribution of the ring-shaped potential to the energy spectra of the Dirac particles. Particular cases of the potentials are also discussed. By considering some particular cases, our results are reduced to the well-known ones presented in the literature. In addition, by taking equal mixture of scalar and vector potentials together with tensor potential, solutions of the Dirac equation are found and then the energy splitting between the two states in the pseudospin doublets is investigated. We indicate that degeneracy between members of pseudospin doublet is removed by tensor interactions. Effects of the potential parameters on the pseudospin doublet splitting are also studied. Radial nodes structure of the Dirac spinor are presented.


Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential, Wei-Hua Potential, Varshni Potential
Arda, Altug; Sever, Ramazan (Walter de Gruyter GmbH, 2014-03-01)
Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any K-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n, K).
Pseudospin and spin symmetry in the Dirac equation with Woods-Saxon potential and tensor potential
AYDOĞDU, OKTAY; Sever, Ramazan (2010-01-01)
The Dirac equation is solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number kappa under pseudospin and spin symmetry. The energy eigenvalues and the Dirac spinors are obtained in terms of hypergeometric functions. The energy eigenvalues are calculated numerically.
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.
Pseudospin symmetry solution of the Dirac equation with an angle-dependent potential
Berkdemir, Cueneyt; Sever, Ramazan (IOP Publishing, 2008-02-01)
The pseudospin symmetry solution of the Dirac equation for spin 1/2 particles moving within the Kratzer potential connected with an angle-dependent potential is investigated systematically. The Nikiforov-Uvarov method is used to solve the Dirac equation. All of the studies are performed for the exact pseudospin symmetry (SU2) case and also the exact spin symmetry case is given briefly in the appendix. Bound-state solutions are presented to discuss the contribution of the angle-dependent potential to the rel...
Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances
AYDOĞDU, OKTAY; Arda, Altug; Sever, Ramazan (2012-04-01)
Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmissi...
Citation Formats
O. Aydoğdu, “Pseudospin symmetry and its applications,” Ph.D. - Doctoral Program, Middle East Technical University, 2009.