Formation of metastabledtμmolecules intμ(2s)−D2collisions

The formation process of metastable $\mathrm{dt}\mu$ molecules in $D_2-T_2$ mixtures in investigated. The $\mathrm{dt}\mu$ molecule exhibits a series of three-body resonances embedded in the $t\mu +d$ scattering continuum just below the $t\mu \mathrm{}\left(2s\right)+d$ threshold. These states can be formed in collisions of excited $t\mu \mathrm{}\left(2s\right)\mathrm{}$ atoms with $D_2$ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of $D_2$. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\mu$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\mu \mathrm{}(n=2\mathrm{})\mathrm{}$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\mu$ can therefore be one of the fastest processes depleting the $n=2\mathrm{}$ levels of the $t\mu$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.