  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.
