# Annihilation energy and decay time of an ortho-Positronium

## TL;DR

This paper models ortho-positronium as a relativistic two-body system in 2+1 dimensions, deriving its energy spectrum, decay energy, and lifetime by analyzing complex energy eigenvalues.

## Contribution

It introduces a novel relativistic two-body approach in 2+1 dimensions to analyze o-Ps, including spin states and decay properties, which is a new perspective compared to traditional methods.

## Key findings

- Calculated annihilation energy of o-Ps
- Determined decay lifetime in the S state
- Derived complex energy spectrum for decay analysis

## Abstract

We approach to the ortho-positronium (o-Ps) as a relativistic two-body problem in $2+1$ dimensions in which o-Ps is composed of two-oppositely charged particles interacting via an attractive Coulomb force. In addition to separation of center of mass and relative coordinates, mapping the background into the polar space-time gives possibility of construction of possible spin eigen-states of o-Ps. This approach makes the energy spectrum complex in order to describe o-Ps that can decay. From the complex energy expression, we find the annihilation energy, binding energy and the life-time of o-Ps, in S state.