Dirac Equation with Unequal Scalar and Vector Potentials under Spin and Pseudospin Symmetry

Atachegbe Clement Onate,Osarodion Ebomwonyi,Michael Chukwudi Onyeaju,Akpan Ndem Ikot

doi:10.4038/sljp.v19i1.8043

Abstract

An approximate solution of the Dirac equation in the D-dimensional space is obtained under spin and pseudospin symmetry limits for the scalar and vector inversely quadratic Yukawa potential within the framework of parametric Nikiforov-Uvarov method using a suitable approximation scheme to the spin-orbit centrifugal term. The two components spinor of the wave function and their energy equations are fully obtained. Some numerical results are obtained for the energy level with various dimensions (D), quantum number (n), vector potential V0 and scalar potential S0 . The results obtained under spin symmetry using either V0 or S0 are equal to the results obtained usingV S 0 0  . But under the pseudospin symmetry, the results obtained using V0 or S0 are not equal to the results obtained usingV S 0 0  .

Highlights

Dirac equation is a relativistic wave equation derived in particle Physics by PaulS(r) are the interacting potentials
In line with the importance and usefulness of the Dirac equation, a great number of studies have been recently devoted to obtain the analytic solutions of the relativistic Dirac equation with the well-known potential models in the framework of the spin and pseudospin symmetry limits in the presence or absence of tensor potential
Hamzavi et al.[32], investigated exactly complete solutions of the Dirac equation with pseudoharmonic potential including linear plus Coulomb-like tensor potential, Suparmi et al.[33,34], studied Dirac equation for scarf and hyperbolic tangent potentials respectivelly, Cari et al.[35], obtained the solutions of Dirac equation for Cotangent potential with a new tensor potential. In all these studies and investigations, the authors considered only the case where the vector potential and scalar potential are equal under spin and pseudospin symmetry respectively

Summary

Introduction

Dirac equation is a relativistic wave equation derived in particle Physics by PaulS(r) are the interacting potentials. In line with the importance and usefulness of the Dirac equation, a great number of studies have been recently devoted to obtain the analytic solutions of the relativistic Dirac equation with the well-known potential models in the framework of the spin and pseudospin symmetry limits in the presence or absence of tensor potential. Onate et al.[17], obtained approximate solutions of the Dirac equation for Second Pӧschl-Teler like scalar and vector potentials with a Coulomb tensor interaction.

Results

Conclusion