# Periodic three-body orbits in the Coulomb potential

## TL;DR

This paper reports the discovery and classification of approximately 100 nonrelativistic, collisionless, periodic three-body orbits in the Coulomb potential, with potential applications in ion trap experiments.

## Contribution

It introduces a new set of Coulomb three-body orbits, classifies them by symmetry and topology, and establishes a linear relation between their periods and topologies.

## Key findings

- Discovered around 100 distinct orbits in Coulomb potential.
- Classified orbits based on symmetry and topology.
- Established a linear relation between period, energy, and topology.

## Abstract

We numerically discovered around 100 distinct nonrelativistic collisionless periodic three-body orbits in the Coulomb potential in vacuo, with vanishing angular momentum, for equal-mass ions with equal absolute values of charges. These orbits are classified according to their symmetry and topology, and a linear relation is established between the periods, at equal energy, and the topologies of orbits. Coulombic three-body orbits can be formed in ion traps, such as the Paul, or the Penning one, where one can test the period vs topology prediction.