Effects of modified woods saxon potential on quantum dynamics of spin 0 scalar particle in a cosmic string spacetime

In this study, we investigate the quantum dynamics of spin-0 scalar particles interacting with both scalar and vector potentials in the background of a cosmic string space-time, under the influence of a quantum flux field. The behavior of the scalar particles is governed by the Klein-Gordon equation, with the scalar and vector potentials taken to be equal and modeled using a modified Woods-Saxon potential-widely applicable across various fields of physics. We derive the radial wave equation in a Schrödinger-like form and analyze the corresponding effective potential of the system. This equation is solved using the confluent hypergeometric function, leading to a quartic equation for the relativistic energy spectrum. Due to the analytical complexity of this equation, we employ numerical methods to explore the energy spectrum. Our results show that the presence of the cosmic string significantly alters the quantum behavior of scalar particles, notably breaking the degeneracy of the energy levels. Furthermore, we examine the combined effects of the quantum flux and the modified Woods-Saxon potential on the energy spectrum and wave functions. The findings indicate that the cosmic string, the quantum flux and the potential play essential roles in shaping the energy eigenvalues and wave function, highlighting their importance in the quantum behavior of scalar particles in topologically nontrivial backgrounds.