A Toy Model for Low Energy Nuclear Fusion

TL;DR

This paper presents a simplified model for low-energy nuclear fusion, suggesting that fusion rates could be significantly enhanced inside a medium compared to free space, potentially enabling observable low-energy fusion reactions.

Contribution

It introduces a toy model using a step potential and discretized energy spectrum to analyze low-energy proton fusion in media, highlighting the potential for observable fusion rates.

Findings

Fusion rate in free space is very small.

Fusion rate in medium can be substantial.

Medium effects can enable low-energy nuclear fusion.

Abstract

We study the fusion of a proton with a nucleus with the emission of two photons at low incident energy of the order of eV or smaller. We use a step model for the repulsive potential between proton and the nuclei. We consider the reaction both in free space and inside a medium. We make a simple model for the medium by assuming a hard wall potential beyond a certain length scale. This essentially leads to discretization of the energy spectrum which is expected inside a medium and is seen both for a crystalline lattice structure and for amorphous materials. We use second order perturbation theory to compute the transition rate. We find that the rate in free space is very small. However in medium, the rate may be substantial. Hence, we conclude that nuclear fusion reactions may take place at low energies at observable rates.