At low temperatures (10–1000 K), negative muons injected into a mixture of deuterium (D) and tritium (T) can catalyze the d+t fusion reaction into helium, which yields a neutron and 17.6 MeV energy. Following the catalyzed reaction, free muons can facilitate another fusion reaction, leading to a cyclic reaction known as muon-catalyzed fusion (μCF), a potential candidate for energy production. μCF has recently regained considerable research interest owing to several new developments and applications. For the nuclear reaction processes, the authors provide an elegant alternative to more complicated coupled-channels (CC) models (Kamimura et al., PRC 107, 034607) by replacing in the transition matrix the exact three-body wave function with a solution that uses a tailored d-t optical potential. The calculated results reproduce well those of the full CC calculations, and the proposed tractable transition-matrix model promises applications to other μCF systems. The predicted low-energy negative muon spectrum will also be useful for the generation of an ultraslow negative muon beam by utilizing the μCF for various applications, such as a scanning negative muon microscope and an injection source for the muon collider.