Radiative lifetime and energy of the low-energy isomeric level in $^{229}$Th

We estimate the range of the radiative lifetime and energy of the anomalous, low-energy $3/2^+(7.8 \pm 0.5$ eV) state in the $^{229}$Th nucleus. Our phenomenological calculations are based on the available experimental data for the intensities of $M1$ and $E2$ transitions between excited levels of the $^{229}$Th nucleus in the $K^{\pi}[Nn_Z\Lambda]=5/2^+[633]$ and $3/2^+[631]$ rotational bands. We also discuss the influence of certain branching coefficients, which affect the currently accepted measured energy of the isomeric state. From this work, we establish a favored region where the transition lifetime and energy should lie at roughly the 90% confidence level. We also suggest new nuclear physics measurements, which would significantly reduce the ambiguity in the present data.