Approximation scheme | An-Najah Staff

Relativistic Bound States in the Presence of Spherically Ring-Shaped Q-Deformed Woods–Saxon Potential With Arbitrary l-States

Tue, 2013-10-29 10:41 — Sameer. Ikhdair

Journal Title, Volume, Page:

International Journal of Modern Physics E Vol. 22, No. 3

Year of Publication:

2013

Link:

http://www.worldscientific.com/doi/abs/10.1142/S0218301313500158

Authors:

SAMEER M. IKHDAIR

Department of Physics, Faculty of Science, An-Najah National University, New Campus, Junaid, Nablus, West Bank, Palestine

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

MAJID HAMZAVI

Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran

A. A. RAJABI

Physics Department, Shahrood University of Technology, Shahrood, Iran

Preferred Abstract (Original):

Approximate bound-state solutions of the Dirac equation with q-deformed Woods–Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term l(l+1)r^-2. Under some limitations, we can obtain solution for the RS Hulthén potential and the standard usual spherical WS potential (q = 1).

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

Sun, 2013-09-15 11:09 — Sameer. Ikhdair

Journal Title, Volume, Page:

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

Year of Publication:

2012

Link:

http://link.springer.com/article/10.2478%2Fs11534-011-0121-5

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

[email protected]

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.