Excitation of the Th229 nucleus by a 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 (London) 617, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogen-like 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 of 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 β²~10^-3. For the $2s$ state the effect is roughly 2 orders of magnitude smaller. An atom with a hole in the $1s$ or $2s$ shell is similar to the hydrogen-like atom, only the hole has a short lifetime τ. After the hole is filled, there is a nonzero 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.