In the muon-catalyzed fusion of most interest, a positively charged deuteron (d), a positively charged triton (t), and a muon essentially form a positively charged muonic molecular heavy hydrogen ion (d–μ–t). The muon, with a rest mass 207 times greater than the rest mass of an electron, is able to drag the more massive triton and deuteron 207 times closer together to each other
 in the muonic (d–μ–t) molecular ion than can an electron in the corresponding electronic (d–e–t) molecular ion. The average separation between the triton and the deuteron in the electronic molecular ion is about one angstrom (100 pm), so the average separation between the triton and the deuteron in the muonic molecular ion is 207 times smaller than that. Due to the strong nuclear force, whenever the triton and the deuteron in the muonic  molecular ion happen to get even closer to each other during their periodic vibrational motions, the probability is very greatly enhanced that the positively charged triton and the positively charged deuteron would undergo quantum tunnelling through the repulsive Coulomb barrier that acts to keep them apart. Indeed, the quantum mechanical tunnelling probability depends roughly exponentially on the average separation between the triton and the deuteron, allowing a single muon to catalyze the d–t nuclear fusion in less than about half a picosecond, once the muonic molecular ion is formed.
The formation time of the muonic molecular ion is one of the "rate-limiting steps" in muon-catalyzed fusion that can easily take up to ten thousand or more picoseconds in a liquid molecular deuterium and tritium mixture (D, DT, T), for example.  Each catalyzing muon thus spends most of its ephemeral existence of 2.2 microseconds, as measured in its rest frame, wandering around looking for suitable deuterons and tritons with which to bind.
Another way of looking at muon-catalyzed fusion is to try to visualize the ground state orbit of a muon around either a deuteron or a triton.  Suppose the muon happens to have fallen into an orbit around a deuteron initially, which it has about a 50% chance of doing if there are approximately equal numbers of deuterons and tritons present, forming an electrically neutral muonic deuterium atom (d–μ) that acts somewhat like a "fat, heavy neutron" due both to its relatively small size (again, 207 times smaller than an electrically neutral electronic deuterium atom (d–e)) and to the very effective "shielding" by the muon of the positive charge of the proton in the deuteron.  Even so, the muon still has a much greater chance of being transferred to any triton that comes near enough to the muonic deuterium than it does of forming a muonic molecular ion.  The electrically neutral muonic tritium atom (t–μ) thus formed will act somewhat like an even "fatter, heavier neutron," but it will most likely hang on to its muon, eventually forming a muonic molecular ion, most likely due to the resonant formation of a hyperfine molecular state within an entire deuterium molecule D (d=e=d), with the muonic molecular ion acting as a "fatter, heavier nucleus" of the "fatter, heavier" neutral "muonic/electronic" deuterium molecule ([d–μ–t]=e=d), as predicted by Vesman, an Estonian graduate student, in 1967.
Once the muonic molecular ion state is formed, the shielding by the muon of the positive charges of the proton of the triton and the proton of the deuteron from each other allows the triton and the deuteron to tunnel through the Coulomb barrier in time span of order of a nanosecond The muon survives the d–t muon-catalyzed nuclear fusion reaction and remains available (usually) to catalyze further d–t muon-catalyzed nuclear fusions.  Each exothermic d–t nuclear fusion releases about 17.6 MeV of energy in the form of a "very fast" neutron having a kinetic energy of about 14.1 MeV and an alpha particle α (a helium-4 nucleus) with a kinetic energy of about 3.5 MeV. An additional 4.8 MeV can be gleaned by having the fast neutrons moderated in a suitable "blanket" surrounding the reaction chamber, with the blanket containing lithium-6, whose nuclei, known by some as "lithions," readily and exothermically absorb thermal neutrons, the lithium-6 being transmuted thereby into an alpha particle and a triton.