Radiative decay of ^229mTh in solid-state nuclear clocks

The ²²⁹Th isotope hosts an exceptionally low-energy nuclear transition in the vacuum ultraviolet range, making it a leading candidate for nuclear optical clocks. Recent laser excitation and fluorescence measurements in Th-doped crystals have demonstrated the feasibility of such clocks, yet the precise lifetime of the nuclear excited state remains uncertain. In this work, we build upon the well-established n³ scaling of M1 nuclear decay rates, which describes how the radiative decay of a magnetic-dipole transition is modified by the refractive index n of an isotropic and homogeneous medium. Our contribution unifies previously disparate experimental results on ²²⁹Th-doped crystals within a single theoretical framework and delineates the conditions under which the scaling remains valid. We further analyze the limitations of extracting vacuum lifetimes from existing solid-state measurements, highlighting the roles of non-radiative decay channels as well as surface and defect-induced effects, which can invalidate the simple n³ rule under realistic experimental conditions. These insights open new possibilities for reducing interrogation times and improving the overall performance of nuclear clocks.