Probability of L -shell nuclear excitation by electronic transitions in 178 Hfm2

We calculate the cross section for the x-ray induced accelerated decay process of the isomer ¹⁷⁸ Hf^m2 ( 16⁺ ,2.446 MeV,31 yr ) via an unknown nuclear state (including the case of a “mixed- K ” state) hypothesized to lie about 10 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 ∼ 10^-32 cm² , a value many orders of magnitude below that needed to explain the results of the isomeric triggering experiments.