Re-evaluation of the Beck et al. data

The currently most accepted value of the isomer energy is 7.8(5) eV, obtained by the so-called “Beck et al. measurement”. In this experiment, researchers from Lawrence Livermore employed a NASA microcalorimeter for a high-resolution gamma measurement of the U-233 decay. Using a clever differencing scheme, they indirectly inferred the energy of the isomer. The final result includes correction terms related to unknown branching ratios.

This measurement is now 10 years old, and in the meantime, no experiment was successful in refining the isomer energy further (there is evidence from the LMU experiment, however, that the isomer energy is between 6.31 and about 18 eV). In particular, two independent experiments at PTB in Germany and UCLA/ALS searched for an optical signal of the isomer using synchrotron radiation to excite nuclei on/in wide bandgap materials, but found no signal. E. V. Tkalya et al. were the first to revisit the Beck et al. measurement and showed that branching ratios markedly different from the ones assumed in the original publication would lead to an isomer energy much larger than 7.8 eV (see their paper here).

Many current experiments have a limited search window, contrained e.g. by the ionization thresholds of Th ions or the transmission window of crystals. Inspired by the mysteriously short lifetime of the Th+ isomer in the LMU experiment, the TU Wien team set out to re-evaluate the original Beck et al. data, aiming to check if the 2007 measurement would be compatible with a much higher isomer energy. Their analysis is now available on the arXiv.

The authors find no major flaw in the original 2007 data analysis. They expand the statistical error of 0.5 eV, which appears to be underestimated, into a two-dimensional contour plot, constructing confidence regions for any given branching ratio. They find that the isomer energy depends only mildly on the branching ratio, in contrast to an earlier analysis by S. L. Zakharov. To give a rough estimate, an isomer energy above 10 eV (below 125 nm) can be excluded at the 95% confidence level.

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Contour plots of branching ratio b (the probability of the 29-keV state to decay out-of-band onto the ground state) vs isomer energy. The horizontal lines represent various values of b that can be found in the literature. The grey shaded region has been scanned in the UCLA@ALS experiment. The three plots assumes different values of the energy splitting of the 42-keV doublet: (d) 198.22 eV, (e) 198.44 eV, and (f) 198.66 eV.