No abstract

No abstract

We report a four-body variational calculation of a hydrogen-like atom consisting of an excited muonic molecule consisting of d, t, and μ, and a ground state electron. Due to the compact size of the muonic molecule dtμ, it behaves as a quasi-nucleus for the electron; however, the system is actually a resonance state because the de-excitation energy of dtμ is sufficient to ionize the electron. We calculate resonance energy levels of the four-body system dtμe using a Gaussian expansion method and a stabilization method. Our best calculation results in a four-body energy of –100.159 88 a.u. which is in good agreement with the value estimated by the first order perturbation theory [Harston et al. Zeitschrift für Physik D 22, 635 (1992)]. We indicate that implementation of the electron-induced polarization of dtμ will be indispensable for the further precise determination of the resonance energy. The present result is the first step towards a full four-body calculation of the muonic molecule under the presence of the electron, which is of importance for development of a muon catalyzed fusion kinetics model.

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.