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

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.