Reaction processes in muon catalyzed fusion ($\mu \mathrm{CF}$), ${\left(dt\mu \right)}_{J=v=0}\to \alpha +n+\mu +17.6\mathrm{MeV}$ or ${\left(\alpha \mu \right)}_{nl}+n+17.6\mathrm{MeV}$ in a deuterium-tritium (D-T) mixture were comprehensively studied by Kamimura, Kino, and Yamashita [Phys. Rev. C 107, 034607 (2023)] by solving the $dt\mu \text{−}\alpha n\mu$ coupled channel (CC) Schrödinger equation under a boundary condition where the muonic molecule ${\left(dt\mu \right)}_{J=v=0}$ was set as the initial state and the outgoing wave was in the $\alpha n\mu$ channel. We approximate this CC framework and propose a considerably more tractable model using the $T$-matrix method based on the Lippmann-Schwinger equation. Nuclear interactions adopted in the $T$-matrix model are determined by reproducing the cross section of the reaction $d+t\to \alpha +n+17.6\mathrm{MeV}$ at low energies. The cross section of the strong-coupling rearrangement reaction is presented in a simple closed form based on our new model. This $T$-matrix model has reproduced most of the calculated results on the above $\mu \mathrm{CF}$ reaction reported by Kamimura et al. (2023) and is applicable to other $\mu \mathrm{CF}$ systems such as $\left(dd\mu \right), \left(tt\mu \right), {\left(dt\mu \right)}^{*}, {\left(dd\mu \right)}^{*}$.

• Received 30 January 2024
• Accepted 10 April 2024

DOI:https://doi.org/10.1103/PhysRevC.109.054625