# Improved Effective Range Expansion for Casimir-Polder potential

## TL;DR

This paper introduces an improved effective range expansion method for analyzing scattering in Casimir-Polder potentials, enhancing accuracy at low energies by leveraging Liouville transformations and potential decomposition.

## Contribution

The authors develop a novel effective range expansion technique that incorporates Liouville transformations and potential decomposition for better low-energy scattering analysis.

## Key findings

- More accurate low-energy scattering amplitudes
- Effective decomposition into elementary problems
- Enhanced theoretical understanding of Casimir-Polder interactions

## 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/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.