Regular Article

Improved effective range expansion for Casimir–Polder potential

Laboratoire Kastler Brossel (LKB), Sorbonne Université, CNRS, ENS-PSL Université, Collège de France, Campus Pierre et Marie Curie, 75252 Paris, France

^a e-mail: pierre-philippe.crepin@polytechnique.org
^b e-mail: romain.guerout@lkb.upmc.fr
^c e-mail: serge.reynaud@lkb.upmc.fr

Received: 16 October 2019
Received in final form: 15 April 2019
Published online: 12 December 2019

Abstract

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/z⁴ 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.