Bound and scattering states in a spacetime with dual topological defects: cosmic string and global monopole

Abstract This paper explores the relativistic quantum motion of scalar bosons in the presence of mixed topological defects: cosmic strings and global monopoles. The Klein–Gordon equation with generalized Coulomb potentials is analyzed in this background. The effects of these topological defects on the equations of motion, phase shifts, and the S-matrix are examined in detail. Bound state solutions are derived from the poles of the S-matrix. We provide analytical expressions for the energy spectrum of bound states, with particular attention to how the parameters of scalar and vector potentials affect the behavior of the system. Furthermore, we explore particular cases involving pure scalar, vector, and mixed scalar–vector potentials, showing how these scenarios impose particular conditions on the existence of bound states. Our results indicate that the solutions obtained associated with scattering and bound states depend significantly on the parameters of the topological defects.