Approximate solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term

Sameer M Ikhdair

doi:10.1063/1.3293759

Abstract

We give the approximate analytic solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term. In the framework of the spin and pseudospin symmetry concept, we obtain the analytic bound state energy spectra and the corresponding two-component upper and lower spinors of the two Dirac particles, in closed form, by means of the Nikiforov–Uvarov method. The special cases of the s-wave κ=±1 (l=l̃=0) Rosen–Morse potential, the Eckart-type potential, the PT-symmetric Rosen–Morse potential, and the nonrelativistic limits are briefly studied.

Highlights

Within the framework of the Dirac equation, the spin symmetry arises if the magnitudes of the attractive scalar potential Srand repulsive vector potential are nearly equal, Srϳ Vrin the nucleii.e., when the difference potential ⌬͑r = Vr − Sr = Cs = const
We show that the spin and pseudospin symmetry Dirac solutions can be reduced to the Sr = Vrand Sr = −Vrin the cases of exact spin symmetry limitation ⌬͑r = 0 and pseudospin symmetry limitation ⌺͑r = 0, respectively
For any spin-orbit coupling centrifugal term ␬, we have found the explicit expressions for energy eigenvalues and associated wave functions in closed form

Summary

INTRODUCTION

The context of spatially dependent mass, we have used and applied a recently proposed approximation scheme[40] for the centrifugal term to find a quasiexact analytic bound state solution of the radial KG equation with spatially dependent effective mass for scalar and vector Hulthén potentials in any arbitrary dimension D and orbital angular momentum quantum number l within the framework of the Nikiforov–UvarovNUmethod.[40–42]. Jia et al.[48] employed an improved approximation scheme to deal with the pseudocentrifugal term to solve the Dirac equation with the generalized Pöschl–Teller potential for arbitrary spin-orbit quantum number ␬. Wei and Dong[51] obtained approximately the analytical bound state solutions of the Dirac equation with the Manning–Rosen for arbitrary spin-orbit coupling quantum number ␬.

NU METHOD

ANALYTIC SOLUTION OF THE DIRAC–ROSEN–MORSE PROBLEM

DISCUSSIONS

CONCLUSIONS