Muon catalyzed fusion (µCF) has recently regained considerable research interest owing to several new developments and applications. In this regard, we have performed a comprehensive study on the most important fusion reaction, namely (dtµ) J=v=0 → α + n + µ + 17.6 MeV or (αµ) nl + n + 17.6 MeV. For the first time, the coupled-channels Schrödinger equation is solved for the reaction, thereby satisfying the boundary condition for the muonic molecule (dtµ) J=v=0 as the initial state and the outgoing wave in the αnµ channel. We employ the dtµ-and αnµ-channel coupled three-body model. All the nuclear interactions, the d-t and α-n potentials, and the dt-αn channel-coupling nonlocal tensor potential are chosen to reproduce the observed low-energy (1 − 300 keV) astrophysical S -factor of the reaction d +t → α+n+17.6 MeV, as well as the total cross section of the α+n reaction at the corresponding energies. The resultant dtµ fusion rate is 1.03 × 10 12 s −1 . Substituting the obtained total wave function into the T -matrix based on the Lippmann-Schwinger equation, we have derived absolute values of the reaction rates going to the individual bound and continuum states of the outgoing α-µ pair. Using these reaction rates, we obtain the initial α-µ sticking probability ω 0 S = 0.857% , which is ∼ 8% smaller than the literature values (≃ 0.92 − 0.93%) , and it is not inconsistent with the most recent observations (2001) at high DT densities. The origin of the 8%-reduction of ω 0 S is that we have employed the outgoing α-n D wave and the dt-αn coupling tensor force. We also calculate the absolute values for the momentum and energy spectra of muons emitted during the fusion process. The most important result is that the peak energy is 1.1 keV although the mean energy is 9.5 keV owing to the long higher-energy tail. This is a useful result for the ongoing experimental project to realize the generation of an ultra-slow negative muon beam by utilizing the µCF for various applications e.g., a scanning negative muon microscope and an injection source for the muon collider.