Scattering and bound states for the Hulth\xe9n potential in a cosmic string background

Mansoureh Hosseinpour,Fabiano M Andrade,Edilberto O Silva,Hassan Hassanabadi

doi:10.1140/epjc/s10052-017-4834-5

Abstract

In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulthén potential and obtain the phase shifts. From the poles of the scattering S-matrix the states energies are determined as well.

Highlights

IntroductionThe most common interpretation known in the literature for this coupling is that of a position-dependent effective mass [8]
To study the relativistic quantum dynamics of particles with spin under the influence of electromagnetic fields in curved spacetime we must consider the modified covariant form of the Dirac equation (h = c = 1) [1,2]iγ μ(x) ∂μ + μ(x) + ie Aμ(x) − M ψ(x) = 0, (1)where Aμ denotes the vector potential associated with the electromagnetic field, μ(x) is the spinor affine connection and γ μ(x) are the Dirac matrices in the curved spacetime
Where Aμ denotes the vector potential associated with the electromagnetic field, μ(x) is the spinor affine connection and γ μ(x) are the Dirac matrices in the curved spacetime

Summary

Introduction

The most common interpretation known in the literature for this coupling is that of a position-dependent effective mass [8] This coupling has been used, for example, to study the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potential in the background spacetime generated by a cosmic string [9]. These couplings are used to study various physical models by including interactions and to investigate their possible physical implications on system dynamics.

Dirac equation in cosmic string background

Scattering analysis

Bound states analysis

Conclusion