Comprehensive study of nuclear reactions in muon catalyzed fusion: I. dt$\mu$ system
Abstract
Muon catalyzed fusion ($\mu$CF) has recently regained considerable research interest owing to several new developments and applications. In this regard, we performed a comprehensive study on the most important fusion reaction, $(dt\mu)_{J=v=0} \to \alpha + n + \mu + 17.6$ MeV or $(\alpha \mu)_{nl} + n + 17.6$ MeV. For the first time, the coupledchannel Schrödinger equation has been solved for the reaction, 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 threebody model. All the nuclear interactions, the $d$$t$ and $\alpha$$n$ potentials, and the $d t$$\alpha n$ channelcoupling nonlocal tensor potential are chosen to reproduce the observed lowenergy astrophysical $S$factor of the reaction $d+t\to \alpha+n + 17.6 \,{\rm MeV}$, as well as the total cross section of the $\alpha+n$ reaction. The resultant $dt\mu$ fusion rate is $1.03 \times 10^{12}\, {\rm s}^{1}$. Substituting the obtained total wave function into the $T$matrix based on the LippmannSchwinger equation, we have derived the reaction rates going to the individual bound and continuum states of the outgoing $\alpha$$\mu$ pair. Using the rates, we obtain the initial $\alpha$$\mu$ sticking probability $\omega_S^0=0.857 \%$, which is consistent with the most recent observations (2001) at high DT densities. We also calculate the momentum and energy spectra of muons emitted during the fusion process. The peak energy is 1.1 keV although the mean energy is 9.5 keV owing to the long higherenergy tail. This is a useful 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.08399
 Bibcode:
 2021arXiv211208399K
 Keywords:

 Nuclear Theory;
 Nuclear Experiment;
 Physics  Atomic Physics;
 Physics  Plasma Physics
 EPrint:
 25 pages, 24 figures. v2: Fig.24 added, minor corrections, submitted to Phys. Rev. C