A key process in the muon-catalysed fusion cycle is a low-energy colli
sion of a t mu atom with a DA molecule, where A is H, D, or T, which l
eads at appropriate incident energies, to the formation of a resonant
complex containing dt mu. In this paper, methods of calculating the re
sonant formation rate of dt mu are discussed. A description is given o
f a new approach that makes use of coupled equations for the rearrange
ment scattering process and elements of Feshbach's theory of resonance
s to obtain an expression for the cross section for resonant dt mu for
mation. The insights gained from this approach are discussed.