Laser excitation of ${}^{229}\mathrm{Th}$ nuclei in doped wide band gap crystals has been demonstrated recently, opening the possibility of developing ultrastable solid-state clocks and sensitive searches for new physics. We develop a quantitative theory of the internal conversion (IC) of isomeric ${}^{229}\mathrm{Th}$ in solid-state hosts and elucidate a crucial requirement in choosing the solid-state hosts in nuclear clock applications. The IC of the isomer proceeds by resonantly exciting a valence band electron to a defect state, accompanied by multiphonon emission. We demonstrate that, if the process is energetically allowed, it generally quenches the isomer on a millisecond timescales, much faster than the isomer’s radiative lifetime, despite ${}^{229}\mathrm{Th}$ being in the $+4$ charge state in the valence band.

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• Atomic, optical & lattice clocks
• Density functional theory
• Nuclear transition rates