On the interaction of a Cornell-type nonminimal coupling with the scalar field under the background of topological defects

In this paper, we investigate the influence of the background of a cosmic string space–time with a distortion of a radial line into a spiral on the interaction of the scalar field with a Cornell-type nonminimal coupling subject to a special static scalar potential. The special static scalar potential consists of radial oscillator harmonics potential and radial inverse-square potential. In order to study such a system based on the Katanaev–Volovich geometric approach, we acquire relativistic solutions corresponding to the generalized Klein–Gordon quantum oscillator for relativistic charged spin-zero boson particles using analytical methods in this background.