Improved Effective Range Expansion for Casimir-Polder potential

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.

References in corpus (7)

• The Casimir force and the quantum theory of lossy optical cavities
• Quantum reflection of helium atom beams from a microstructured grating
• Casimir-Polder shifts on quantum levitation states
• Quantum reflection of antihydrogen from a liquid helium film
• Quantum interference test of the equivalence principle on antihydrogen
• Quantum reflection and Liouville transformations from wells to walls
• Liouville transformations and quantum reflection

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