# Positron Binding and Annihilation in Alkane Molecules

## TL;DR

This paper introduces a model to study how positrons bind and annihilate with alkane molecules, predicting binding energies and annihilation rates that align with experimental data, including a second bound state for larger alkanes.

## Contribution

A novel model-potential approach for calculating positron binding energies and annihilation rates in alkane molecules, predicting a second bound state for larger alkanes.

## Key findings

- Calculated binding energies agree with experimental data.
- Predicted existence of a second bound state for n-alkanes with n≥12.
- Annihilation rate scales with the square root of binding energy.

## Abstract

A model-potential approach has been developed to study positron interactions with molecules. Binding energies and annihilation rates are calculated for positron bound states with a range of alkane molecules, including rings and isomers. The calculated binding energies are in good agreement with experimental data, and the existence of a second bound state for $n$-alkanes (C$_n$H$_{2n+2}$) with $n\geq12$ is predicted in accord with experiment. The annihilation rate for the ground positron bound state scales linearly with the square root of the binding energy.