Hill regions of charged three-body systems

TL;DR

This paper analyzes the admissible configurations and orientations of charged three-body systems, such as helium and electron-positron systems, using symmetry reduction and compares them to gravitational three-body systems.

Contribution

It introduces a framework for studying charged three-body systems' configurations based on symmetry reduction, extending previous gravitational models.

Findings

Identified admissible configurations for specific charged systems.

Compared charged systems with gravitational three-body systems.

Provided a systematic approach for analyzing charged three-body dynamics.

Abstract

For charged three-body systems, we discuss the configurations and orientations that are admissible for given values of the conserved total energy and angular momentum. The admissible configurations and orientations are discussed on a configuration space that is reduced by the translational, rotational and dilation symmetries of charged three-body systems. We consider the examples of the charged three-body systems given by the helium atom (two electrons and a nucleus) and the compound of two electrons and one positron. For comparison, the well known example of the Newtonian gravitational three-body system is discussed for the scheme presented in this paper first.