Importance of fluctuations of cross sections in muon-catalysed t-t fusion reactions

TL;DR

This paper investigates how fluctuations in cross sections, caused by muons, influence the reaction rate of muon-catalyzed t-t fusion, highlighting the importance of these fluctuations in theoretical models.

Contribution

It introduces a model that accounts for cross section fluctuations due to muons in calculating the reaction rate of muon-catalyzed t-t fusion.

Findings

Calculated reaction rate is 5.0×10⁻³ μs⁻¹.

Reaction rate is significantly lower than experimental muonic cycling rate.

Cross section fluctuations have a substantial impact on reaction rate estimates.

Abstract

We discuss the reaction rate of the muon-catalysed $t$-$t$ fusion. The reaction rate is determined as a function of the temperature using the model of "in flight" fusion. We especially take into account the effect of the fluctuation of the cross section due to the existence of the muon. The obtained reaction rate 5.0$\times10^{-3} \mu$s$^{-1}$ is a factor of 10$^{-3}$ smaller than the experimental muonic cycling rate in the solid tritium target.