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:

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.