Hyperfine structure splitting of the ground states in the $pd\mu ,pt\mu$ and $dt\mu$ ions

The hyperfine structure splittings of the ground states of the $pd\mu ,pt\mu$ and $dt\mu$ ions are determined with the use of highly accurate expectation values of the interparticle delta-functions obtained in recent computations. The corresponding hyperfine structure splittings, e.g., ${\mathrm{\Delta }}_{12}=$ 1.3400149$\cdot {10}^7$ $MHz$ and ${\mathrm{\Delta }}_{23}=$ 3.3518984$\cdot {10}^7$ $MHz$ for the $pt\mu$ ion, can directly be measured in modern experiments.