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Scalar bosons with Coulomb potentials in a cosmic string background: Scattering and bound states

The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^μ$ and nonminimal $X^μ$) and scalar ($V_{s}$) interactions embedded in the background of a cosmic string is explored in the context of the Klein-Gordon equation. Considering Coulomb interactions, the effects of this topological defect in equation of motion, phase shift and S-matrix are analyzed and discussed. Bound-state solutions are obtained from poles of the S-matrix and it is shown that bound-state solutions are possible only for a restrict range of coupling constants.