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

TL;DR

This paper investigates how scalar bosons behave under Coulomb potentials in a cosmic string background, analyzing scattering and bound states within the Klein-Gordon framework, revealing topological effects on quantum states.

Contribution

It provides a detailed analysis of Coulomb interactions for scalar bosons in a cosmic string background, including phase shifts, S-matrix, and bound states, highlighting the influence of topology.

Findings

Bound states exist only within a restricted range of coupling constants.

Cosmic string topology affects phase shifts and scattering properties.

Bound-state solutions are derived from S-matrix poles.

Abstract

The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^{\mu}$ and nonminimal $X^{\mu}$) 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.