Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

TL;DR

This paper investigates how a mixed vector-scalar smooth step potential affects scattering and bound states of a spinless particle, revealing the influence of scalar backgrounds and simplifying the eigenenergy problem.

Contribution

It introduces a novel analysis of scattering and bound states in a mixed potential, mapping the problem to a Schrödinger-like equation with an effective Rosen-Morse potential and simplifying the eigenenergy calculation.

Findings

Scalar background significantly influences bound state formation.

Eigenenergies are obtained by solving an algebraic equation instead of differential equations.

The approach simplifies analyzing spinless particle interactions in complex potentials.

Abstract

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schr\"{o}dinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation.