On the weakly-bound (1,1)-states in the three-body d d μ and d t μ muonic ions

The both total and binding energies of the (1,1)-states in the weakly-bound three-body muonic $d d \mu$ and $d t \mu$ ions are determined to high numerical accuracy. The binding energy of the (1,1)-state in the muonic $d t \mu$ ion is evaluated as $\varepsilon(d t \mu)$ = -0.66033003831(30) $eV$, while for the same state in the muonic $d d \mu$ 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.