Comprehensive study of muon-catalyzed nuclear reaction processes in the dt? molecule

Muon catalyzed fusion (mu CF) has recently regained considerable research interest owing to several new developments and applications. In this regard, we have performed a comprehensive study of the most important fusion reaction, namely, (dt mu)J=v=0 -> alpha + n + mu + 17.6 MeV or (alpha mu)nl + n + 17.6 MeV. The coupled - channel Schrodinger equation for the reaction is thus solved, satisfying the boundary condition for the muonic molecule (dt mu)J=v=0 as the initial state and the outgoing wave in the alpha n mu channel. We employ the dt mu- and alpha n mu-channel coupled three-body model. All the nuclear interactions, the d -t and alpha-n potentials, and the dt-alpha n channel-coupling nonlocal tensor potential are chosen to reproduce the observed low-energy (1-300 keV) astrophysical S factor of the reaction d + t -> alpha + n + 17.6 MeV, as well as the total cross section of the alpha + n reaction at the corresponding energies. The resultant dt mu fusion rate is1.15x1012 s-1. Substituting the obtained total wave function into the T matrix based on the Lippmann-Schwinger equation, we have calculated absolute values of the fusion rates lambda bound f and lambda cont. f going to the bound and continuum states of the outgoing alpha-mu pair, respectively. We then derived the initial alpha-mu sticking probability omega 0S= lambda boundf/(lambda boundf + lambda cont. f )=0.857%, which is approximate to 7% smaller than the literature values (approximate to 0.91%-0.93%) and can explain the recent observations (2001) at high D-T densities. We have much improved the sticking-probability calculation by employing the D-wave alpha-n outgoing channel with the nonlocal tensor-force dt-alpha n coupling and by deriving omega 0S based on the absolute values of the lambda bound f and lambda cont. f. We also calculate the absolute values for the momentum and energy spectra of the muon 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 an essential result for the ongoing experimental project to realize the generation of an ultraslow negative muon beam by utilizing the mu CF for various applications, e.g., a scanning negative muon microscope and an injection source for the muon collider.