Examination of a key resonant process in the muon-catalysed fusion cycle that can be treated theoretically in the same way as a chemical reaction

Abstract

The muon-catalysed fusion cycle, the sequence of processes whereby a negatively charged muon in a deuterium–tritium mixture at room temperature catalyses nuclear fusion reactions, is first described. A key process in this cycle is a low-energy collision of a tµ atom with a DA molecule, where A is D, H or T, which leads at appropriate incident energies, to the formation of a resonant complex containing dtµ. A description is given of methods that have been used so far to calculate, λ _dtµ , the resonant formation rate of dtµ. A new theoretical approach involving close-coupling equations and elements of Feshbach's theory of resonances is discussed. It is shown how close-coupling methods, such as that developed by Pack and Parker to calculate the rates of chemical reactions involving three atoms, can be applied to the calculations of λ _dtµ .