# Single Particle Closed Orbit in Yukawa Potential

## TL;DR

This paper investigates the motion of a single particle in a Yukawa potential, demonstrating how the precession and shape of orbits can be controlled by tuning the coupling parameter, including conditions for closed orbits.

## Contribution

It provides a detailed analysis of particle orbits in Yukawa potential, identifying parameters for closed and petal-shaped bound orbits, and calculating the threshold energy for bound states.

## Key findings

- Precessing elliptical orbits observed and tunable via coupling parameter.
- Conditions for closed bound orbits identified.
- Threshold energy for orbit boundness calculated.

## Abstract

We study the orbit of a single particle moving under the Yukawa potential and observe the precessing ellipse type orbits. The amount of precession can be tuned through the coupling parameter $\alpha$. With a suitable choice of the coupling parameter; we can get a closed bound orbit. In some cases we have observed some petals which can also have a closed bound nature with an appropriate choice of the coupling constant. A threshold energy has also been calculated for the boundness of the orbits.