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The non-resonant formation of $dd\mu$ molecules in the loosely bound state incollisions of non-thermalized $d\mu$ atoms with deuterium molecules D$_2$ hasbeen considered. The process of such a type is possible only for collisionenergies exceeded the ionization potential of D$_2$. The calculated rates of$dd\mu$ formation in the above-threshold energy region are about one order ofmagnitude higher than obtained earlier.  The role of epithermal non-resonant $\mu$-molecule formation for the kineticsof $\mu$CF processes in D$_2$ gas was studied. It was shown that thenon-resonant $dd\mu$ formation by $d\mu$ atoms accelerated during the cascadecan be directly observed in the neutron time spectra at very short initialtimes.

Influence of epithermal muonic molecule formation on kinetics of the $\mu$CF processes in deuterium