Excitation of the ^229Th nucleus by the hole in the inner electronic shells

The ^229Th nucleus has a long-lived isomeric state A^* at 8.338(24) eV [Kraemer et al, Nature, 617, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogenlike Th ion in the 1s state the hyperfine structure splitting is about 0.7 eV. This means that the hyperfine interaction can mix the nuclear ground state with the isomeric state with a mixing coefficient β about 0.03. If the electron is suddenly removed from this system, the nucleus will be left in the mixed state. The probability to find the nucleus in the isomeric state A^* is equal to β^2∼ 10^-3. For the 2s state the effect is roughly two orders of magnitude smaller. An atom with a hole in the 1s or 2s shell is similar to the hydrogenlike atom, only the hole has a short lifetime τ. After the hole is filled, there is a non-zero probability to find the nucleus in the A^* state. Estimates of this probability are presented along with a discussion of possible experiments on Th-doped xenotime-type orthophosphate crystals and other broad band gap materials.