On the weakly-bound (1,1)-states in the three-body $dd\mu$ and $dt\mu$ muonic ions

The both total and binding energies of the (1,1)-states in the weakly-bound three-body muonic $dd\mu$ and $dt\mu$ ions are determined to high numerical accuracy. The binding energy of the (1,1)-state in the muonic $dt\mu$ ion is evaluated as $\epsilon (dt\mu )$ = -0.66033003831(30) $eV$, while for the same state in the muonic $dd\mu$ ion we have found that $\varepsilon(d d \mu)$=-1.9749806166970(30)$eV$. These energies are the most accurate numerical values obtained for these systems and they are sufficient for all current and future experimental needs.