# Scattering theory of the screened Casimir interaction in electrolytes

## TL;DR

This paper develops a scattering theory framework to analyze the Casimir interaction between dielectric surfaces separated by electrolytes, incorporating nonlocal responses and ion effects, revealing screening behaviors at different frequencies.

## Contribution

It introduces a comprehensive scattering approach accounting for both transverse and longitudinal electromagnetic modes in electrolytes, including ion-induced screening effects.

## Key findings

- Long-distance Casimir interaction is dominated by unscreened transverse-magnetic modes.
- Longitudinal channel contributions are screened over the Debye length.
- Zero-frequency interactions include both screened longitudinal and unscreened transverse components.

## Abstract

We apply the scattering approach to the Casimir interaction between two dielectric half-spaces separated by an electrolyte solution. We take the nonlocal electromagnetic response of the intervening medium into account, which results from the presence of movable ions in solution. In addition to the usual transverse modes, we consider longitudinal channels and their coupling by reflection at the surface of the local dielectric. The Casimir interaction energy is calculated from the matrix describing a round-trip of coupled transverse and longitudinal waves between the interacting surfaces. The nonzero-frequency contributions are approximately unaffected by the presence of ions. We find, at zero frequency, a contribution from longitudinal channels, which is screened over a distance of the order of the Debye length, alongside an unscreened term arising from transverse-magnetic modes. The latter defines the long-distance asymptotic limit for the interaction.