Journal Title, Volume, Page:

Central European Journal of Physics , Volume 10, Issue 2, pp 361-381
Year of Publication:

2012
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.

Journal Title, Volume, Page:

Cent. Eur. J. Phys., 8(4), 652-666
Year of Publication:

2010
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.

Journal Title, Volume, Page:

Journal of Mathematical Physics, Vol. 53 Issue 8, p082101
Year of Publication:

2012
Preferred Abstract (Original):

We approximately investigated pseudospin symmetric
solutions of the Dirac equation for attractive radial potential,
including a Coulomb-like tensor interaction under pseudospin symmetry
limit for any spin-orbit quantum number κ. By using the parametric
generalization of the Nikiforov-Uvarov method, the energy eigenvalues
equation and the corresponding wave functions have been obtained in
closed forms. Some numerical results are also given. We presented tensor
interaction removes degeneracy between two states in pseudospin
doublets.

Journal Title, Volume, Page:

Applied Mathematics and Computation, 216, 545–555
Year of Publication:

2010
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.