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

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.