Role of resonance states of muonic molecule in muon catalyzed fusion

Muon catalyzed fusion (μCF) is a cyclic reaction where a negatively charged muon itself acts like a catalyst of nuclear fusion between hydrogen isotopes. In the μCF reaction, muon transfer from deuteron to triton and muonic molecular formation are rate-limiting processes. In this work, we have investigated the role of resonance states of muonic molecule in the μCF which affects the muonic deuterium atom population. Solving simultaneous rate equations numerically by the fourth-order Runge-Kutta method, we determined the muonic molecular formation rate so that the number of fusion events reproduces a latest experimental result. It is revealed that the resonance states play a role to enhance the fusion rate by accelerating the de-excitation of the muonic atoms.