  We study the effective range expansion of scattering on a real Casimir-Polder
potential. We use Liouville transformations which transform the potential
landscape while preserving the reflection and transmission amplitudes. We
decompose the scattering calculation in two more elementary problems, one for
the homogeneous 1/z^4 potential and the other one for the correction to this
idealization. We use the symmetries of the transformed problem and the
properties of the scattering matrices to derive an improved effective range
expansion leading to a more accurate expansion of scattering amplitudes at low
energy.
