Theoretical evaluation of decay mode of $ {}^{229m} \mathrm{Th} $ in solid samples

The excitation energy of ${}^{229m} \mathrm{Th}$ is extremely low at $8.4 \, \mathrm{eV}$; thus, this isotope exhibits changes in its decay modes depending on the chemical state, specifically the outermost electronic states. However, the reported half-lives of the $\gamma$-ray transition are not consistent among the previous experiments. In this study, we investigate the chemical states of ${}^{229m} \mathrm{Th}$ by density functional theory calculations. Based on these results, we evaluate the relationship between the experimental half-life of each sample and the electronic state of $\mathrm{Th}$. The calculation results indicate that ion trap method, $\mathrm{Ca} \mathrm{F}_2$ model and $\mathrm{Mg} \mathrm{F}_2$ one decay only via the $\gamma$-ray transition, whereas $\mathrm{Li} \mathrm{Sr} \mathrm{Al} \mathrm{F}_6$ one decays via the $\gamma$-ray transition and has a possibility of decay via internal conversion and electron bridge.