Spin and pseudospin symmetries of a relativistic fermion in an elastic medium with spiral dislocations
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Spin and pseudospin symmetries of a relativistic fermion in an elastic medium with spiral dislocations S. Zare1,a , H. Hassanabadi1,b , G. J. Rampho2,c , A. N. Ikot2,3,d 1 Faculty of Physics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran 2 Department of Physics, University of South Africa, Florida 1710, Johannesburg, South Africa 3 Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Nigeria
Received: 7 June 2020 / Accepted: 15 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we investigate a relativistic fermion in an elastic medium as well as a linear topological defect by focusing on the spiral dislocation. Then, we solve the coupled Dirac equation in the presence of scalar and vector potentials. We investigate two special cases by focusing on a spin symmetry limit and a pseudospin symmetry limit. After considering a fermion based on the Dirac equation in the background of spiral dislocation, by considering two special cases, in the presence of oscillator and Kratzer-like potentials, we find the energy eigenvalues according to the wave functions by using of analytical methods.
1 Introduction Dislocations and disclinations are topological defects that specify the presence of torsion in the elastic medium [1–9]. A topological defect space-times have brought a major interest in gravitation and quantum field theory which remarkable points have been raised concerning quantum effects in different scenarios. The screw dislocation and the spiral dislocation [10] are the branches of dislocations. Dislocations were investigated in terms of differential geometry by many researchers. For example, the authors of Ref. [11] have analyzed the interaction of a scalar field with a Coulomb-type potential in the space-time with a screw dislocation. On the other hand, according to the Katanaev–Volovich research, dislocation on quantum systems that is a principle from the attendance of an edge dislocation (a spiral dislocation) in an elastic medium has been reported recently, for example in studies of an Abelian geometric phase in relativistic and nonrelativistic quantum dynamics [12] and the harmonic oscillator in an elastic medium [13]. In Refs. [14–19], we can point to other works that have been done in the background of topological defects. According to the spin character of particles in the relativistic regime, the motion of particles is generally examined by using either the Klein–Gordon or the Dirac equation [20,21]. Thus, the spin-half particle like an electron is examined by the Dirac equation. In theoretical physics, the Dirac equation has been considered by researchers in many branches of physics
a e-mail: [email protected] b e-mail: [email protected] (corresponding author) c e-mail: [email protected] d e-mail: [email protected]
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