# Thick shell regime in the chameleon two-body problem

## TL;DR

This paper refines the analysis of chameleon theories in the thick shell regime, accounting for the influence of test and source bodies on the chameleon field, leading to more accurate force predictions and tighter experimental bounds.

## Contribution

It introduces an improved approximation for the chameleon potential in the thick shell regime, enhancing the accuracy of force calculations and constraints on model parameters.

## Key findings

- Derived more restrictive bounds on chameleon model parameters.
- Showed composition-dependent acceleration even with universal couplings.
- Enhanced theoretical predictions align better with lunar laser ranging data.

## Abstract

In a previous paper [Phys. Rev. D 97, 104044 (2018)] we pointed out some shortcomings of the standard approach to chameleon theories consisting in treating the small bodies used to test the weak equivalence principle (WEP) as test particles, whose presence do not modify the chameleon field configuration. In that paper we developed an alternative method to determine the relevant field configuration which takes into account the influence of both test and source bodies, and computed the chamaleon mediated force. Relying on that analysis we showed that the effective acceleration of test bodies is composition dependent even when the model is based on universal couplings. In this paper, we improve our method by using a more suitable approximation for the effective chameleon potential in situations where the bodies are in the so-called "thick shell regime". We then find new and more restrictive bounds on the model' s parametres by confronting the new theoretical predictions with the empirical bounds on E\"otv\"os parameter comming from the lunar laser ranging experiments.