Scattering and bound states of Dirac Equation in presence of cosmic string for Hulth\'en potential

TL;DR

This paper investigates the Dirac equation in a cosmic string spacetime with Hulthén potential, deriving scattering states, phase shifts, and bound state energies using an approximation method.

Contribution

It introduces a novel solution approach for the Dirac equation with Hulthén potential in cosmic string spacetime, including scattering and bound state analysis.

Findings

Derived phase shifts for scattering states.

Calculated bound state energies from S-matrix poles.

Provided approximate solutions for the radial Dirac equation.

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 Hulth\'{e}n potential and obtain the phase shifts. From the poles of the scattering $S$-matrix the states energies are determined as well.