  We explore the effects arising due to the coupling of the center of mass and
relative motion of two charged particles confined on an inhomogeneous helix
with a locally modified radius. It is first proven that a separation of the
center of mass and the relative motion is provided if and only if the confining
manifold represents a homogeneous helix. In this case bound states of
repulsively Coulomb interacting particles occur. For an inhomogeneous helix,
the coupling of the center of mass and relative motion induces an energy
transfer between the collective and relative motion, leading to dissociation of
initially bound states in a scattering process. Due to the time reversal
symmetry, a binding of the particles out of the scattering continuum is thus
equally possible. We identify the regimes of dissociation for different initial
conditions and provide an analysis of the underlying phase space via Poincar\'e
surfaces of section. Bound states inside the inhomogeneity as well as resonant
states are identified.
