Cross-sections of muon-catalyzed fusion reactions

Muon-catalyzed nuclear fusion reactions in-flight have long been overshadowed by fusion from molecular states, primarily due to the perception that their reaction rates are lower than the free muon’s lifetime. The total cross-sections of reactions catalyzed by [Formula: see text]-muons exceed those of uncatalyzed reactions and constitute a primary focus of theoretical modeling efforts. In this work, three microscopic models are presented for the mirror reactions [Formula: see text]n 4 He and [Formula: see text]He[Formula: see text]p 4 He. These models are employed to numerically solve the Faddeev integral three-body equations for systems of the type [Formula: see text] and [Formula: see text], where [Formula: see text], in momentum space. The Coulomb interaction is accounted for in a two-potential scheme. The ratio of the three-body cross-sections calculated for the muon and the electron is used to infer the role of the muon in in-flight nuclear fusion. Finally, the obtained cross-sections are utilized to compare the power generated by catalyzed reactions with the bremsstrahlung power losses of the electron in a plasma environment.