Estimation of radiative half-life of Th 229 m by half-life measurement of other nuclear excited states in Th 229

We perform coincidence measurements between \ensuremath{\alpha} particles and \ensuremath{\gamma} rays from a $^{233}\mathrm{U}$ source to determine the half-lives of the excited state in a $^{229}\mathrm{Th}$ nucleus. We first prove that the half-lives of 42.43- and 164.53-keV states are consistent with literature values, whereas that of the 97.14-keV state [93(7) ps] deviates from a previously measured value [147(12) ps]. The half-lives of 71.83- and 163.25-keV states are determined for the first time. Based on the obtained half-lives and the Alaga rule, we estimate the radiative half-life of the low-energy isomeric state $(^{229m}\mathrm{Th})$ to be $5.0(11)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ s, which is one of the key parameters for the frequency standard based on $^{229}\mathrm{Th}$.