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Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic String Spacetime with Torsion, Curvature, and a Coulomb Potential

Abdelmalek Boumali

TL;DR

The paper develops a unified analytical framework for Dirac scattering of spin-1/2 particles in a spinning cosmic-string spacetime with conical curvature and torsion, both with and without a Coulomb potential. Central to the approach are the geometry-induced modifications to the effective azimuthal quantum number $\kappa_{eff}(\alpha)$ and the geometry-driven radial cutoff $\rho_c$, which together shape radial solutions, phase shifts, and cross sections. Across several configurations—pure string, balanced torsion, pure rotation, screw dislocations, and the general case—the authors derive closed-form radial solutions (in terms of confluent hypergeometric and Bessel functions) and reveal Aharonov-Bohm-like contributions, energy- and momentum-dependent asymmetries, and topology-renormalised Mott/Rutherford patterns. They also discuss possible experimental analogues in Dirac materials, such as graphene, where lattice defects emulate cosmic-string geometry and render the predicted scattering effects observable at tabletop scales.

Abstract

This paper investigates the scattering states of spin-1/2 particles in the spacetime of a spinning cosmic string with spacelike disclination and dislocation, with and without a Coulomb interaction. Working within the tetrad formalism, we solve the Dirac equation for several configurations of the angular momentum density $J_t$ and the torsion parameter $J_z$ that are relevant from a physical perspective. These configurations include balanced torsion ($J_t = J_z$), pure spinning strings ($J_z = 0$), pure screw dislocations ($J_t = 0$) and the general case. In all cases, the geometry modifies an effective azimuthal quantum number, and for strong rotation it introduces a geometric radial cutoff $ρ_c$ that acts as a hard wall. These factors lead to closed-form expressions for the radial wave functions, phase shifts and differential cross sections, which are expressed in terms of confluent hypergeometric and Bessel functions. We demonstrate that conical curvature, rotation and torsion generate Aharonov-Bohm-like contributions, as well as energy- and momentum-dependent asymmetries in Dirac-Coulomb scattering. This results in topology-renormalised Mott/Rutherford patterns. In the Coulomb-free limit, scattering becomes purely geometric yet still exhibits characteristic forward enhancement, which is governed by defect parameters and the cutoff. We briefly discuss possible realisations in Dirac materials, such as strained or defective graphene, where lattice disclinations and dislocations mimic the cosmic-string geometry.

Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic String Spacetime with Torsion, Curvature, and a Coulomb Potential

TL;DR

The paper develops a unified analytical framework for Dirac scattering of spin-1/2 particles in a spinning cosmic-string spacetime with conical curvature and torsion, both with and without a Coulomb potential. Central to the approach are the geometry-induced modifications to the effective azimuthal quantum number and the geometry-driven radial cutoff , which together shape radial solutions, phase shifts, and cross sections. Across several configurations—pure string, balanced torsion, pure rotation, screw dislocations, and the general case—the authors derive closed-form radial solutions (in terms of confluent hypergeometric and Bessel functions) and reveal Aharonov-Bohm-like contributions, energy- and momentum-dependent asymmetries, and topology-renormalised Mott/Rutherford patterns. They also discuss possible experimental analogues in Dirac materials, such as graphene, where lattice defects emulate cosmic-string geometry and render the predicted scattering effects observable at tabletop scales.

Abstract

This paper investigates the scattering states of spin-1/2 particles in the spacetime of a spinning cosmic string with spacelike disclination and dislocation, with and without a Coulomb interaction. Working within the tetrad formalism, we solve the Dirac equation for several configurations of the angular momentum density and the torsion parameter that are relevant from a physical perspective. These configurations include balanced torsion (), pure spinning strings (), pure screw dislocations () and the general case. In all cases, the geometry modifies an effective azimuthal quantum number, and for strong rotation it introduces a geometric radial cutoff that acts as a hard wall. These factors lead to closed-form expressions for the radial wave functions, phase shifts and differential cross sections, which are expressed in terms of confluent hypergeometric and Bessel functions. We demonstrate that conical curvature, rotation and torsion generate Aharonov-Bohm-like contributions, as well as energy- and momentum-dependent asymmetries in Dirac-Coulomb scattering. This results in topology-renormalised Mott/Rutherford patterns. In the Coulomb-free limit, scattering becomes purely geometric yet still exhibits characteristic forward enhancement, which is governed by defect parameters and the cutoff. We briefly discuss possible realisations in Dirac materials, such as strained or defective graphene, where lattice disclinations and dislocations mimic the cosmic-string geometry.

Paper Structure

This paper contains 24 sections, 60 equations, 5 figures.

Table of Contents

  1. Introduction
  2. DIRAC equation IN THE COSMIC STRING BACKGROUND
  3. First case: Dirac equation in a Spinning Cosmic String Background with Equal Angular Momentum and Torsion ($j^{2}=0$)
  4. Second case: Dirac equation in a Purely Spinning Cosmic String Background ($J^{z}=0$)
  5. Third case: Dirac equation in a Cosmic String Background with Screw Dislocations ($J^{t}=0$)
  6. General case: Dirac equation in a Torsion and Curvature-Modified Spacetime
  7. Scattering States Under Coulomb Potential
  8. Pure cosmic string $J_{t}=J_{z}=0$
  9. Asymptotics and phase shifts
  10. Balanced Torsion $j^{2}=0,|J_{z}|=|J_{t}|=J$
  11. Purely Spinning Cosmic String $J_{z}=0$
  12. Screw Dislocations $J_{t}=0$
  13. General Case: Torsion and Curvature-Modified Spacetime
  14. Discussion
  15. Geometric scattering in no electromagnetic potential
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Differential and Total Cross Sections for Spin-1/2 Scattering in Pure Cosmic String Spacetime (No Torsion or Rotation)
  • Figure 2: Differential and Total Cross Sections for Spin-1/2 Scattering in Balanced Torsion Cosmic String Spacetime (J_t = J_z)
  • Figure 3: Differential and Total Cross Sections for Spin-1/2 Scattering in Pure Spinning Cosmic String Spacetime (J_z = 0)
  • Figure 4: Differential and Total Cross Sections for Spin-1/2 Scattering in Screw Dislocation Cosmic String Spacetime (J_t = 0)
  • Figure 5: Spacetime Geometric Effects on Scattering Cross Sections in Four Classes of Cosmic String Models in the absence of a Coulomb potential