Excitation of the ${}^{229}\mathrm{Th}$ nucleus by a hole in the inner electronic shells

The ${}^{229}\mathrm{Th}$ 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 $\beta$ 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 ${\beta }^2\sim {10}^{-3}$. 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 $\tau$. 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.

Figure 1

Schematic level structure of ${}^{229}\mathrm{Th}$ ion with a hole in the inner $\mathrm{ns}$ shell, $n=1,2$. $\mathrm{\Delta }\approx 8.3$ eV is the energy of the isomeric nuclear state $A^{*}(I^{\pi }={\frac{3}{2}}^{+})$. Blue dashed lines are allowed transitions of the hole to the $(n+1)p$ shell. The hyperfine splittings for the two nuclear states are comparable, while for the electronic $(n+1)p$ state it is much smaller than for $ns$ state. The fine structure for the $p$ shell is not shown.