Decay rates of excited muonic molecular ions

Muonic molecular ions in excited states have been predicted to form in collisions between excited muonic atoms and hydrogen molecules. We have calculated radiative and Coulombic decay rates for $\mathrm{pp}{\mu }^{*}$ and $\mathrm{dd}{\mu }^{*}$ molecular states located below the $2s$ threshold, using the complex rotation method. The x-ray spectrum from the radiative decay is shown to exhibit several maxima, corresponding to the vibrational motion of the decaying molecule. The branching ratio of the radiative decay mode was calculated to be less than 15% for $\mathrm{pp}{\mu }^{*},$ while a radiative yield of more than 80% is predicted for the decay of $\mathrm{dd}{\mu }^{*}.$ Our results have a significant impact on the analysis of the muon catalyzed fusion cycle as well as on the interpretation of exotic hydrogen spectroscopy.