Probability ofL-shell nuclear excitation by electronic transitions inHfm2178

We calculate the cross section for the x-ray induced accelerated decay process of the isomer ${}^{178}\mathrm{Hf}^{m2}\left({16}^{+},2.446\text{MeV},31\text{yr}\right)$ via an unknown nuclear state (including the case of a “mixed-$K$” state) hypothesized to lie about $10\text{keV}$ in energy above the isomer. The excitation of the 31 yr isomer to an intermediate level is assumed to proceed via an electronic transition between atomic shells as has been recently postulated to explain the observation of “triggering” of the decay of the isomer by irradiation with x rays. The accelerated decay cross section is calculated in the most favorable case to be $\sim {10}^{-32}{\text{cm}}^2$, a value many orders of magnitude below that needed to explain the results of the isomeric triggering experiments.