On the influence of Maxwell--Chern--Simons electrodynamics in nuclear fusion involving electronic and muonic molecules

TL;DR

This paper investigates whether Maxwell--Chern--Simons electrodynamics can enhance nuclear fusion rates in electronic and muonic molecules, finding negligible effects for muonic molecules but potential improvements for electronic molecules.

Contribution

It provides a quantitative analysis of Maxwell--Chern--Simons effects on nuclear fusion probabilities in different molecular systems, comparing with other interaction models.

Findings

No significant fusion rate enhancement in muonic molecules.

Potential fusion rate improvements in electronic molecules.

Numerical predictions for various molecular fusion and tunneling rates.

Abstract

New results recently obtained (\textit{Annals of Physics} (New York) a.n.~168943) established some non-relativistic ground state solutions for three-body molecules interacting through a Chern--Simons model. Within this model, it was argued that Chern--Simons potential should not help improve the fusion rates by replacing electrons with muons, in the case of particular muonic molecules. This achievement motivated us to investigate quantitatively whether or not the Maxwell--Chern--Simons electrodynamics could influence positively, for example, the probability of having a muon-catalyzed fusion; its contribution to electronic molecules is also considered in this letter. The principal factors related to the probability of elementary nuclear fusion are therefore numerically calculated and compared with their analogs admitting other forms of interaction like $-1/\rho$ and $\ln (\rho)$. The analysis carried on here confirms that one should not expect a significant improvement in nuclear fusion rates in the case of muonic molecules, although, surprisingly, the same is not true for electronic molecules, compared with other theoretical predictions. Numerical predictions for the fusion rates for $ppe$, $pp\mu$, $dde$ and $dd\mu$ molecules are given as well as the predicted value for the tunneling rate for these molecules.