Direct measurement of the terrestrial $^7$Be $L/K$ capture ratio in cryogenic tantalum

We report a high-statistics measurement of the $L/K$ orbital electron capture (EC) ratio in $^7$Be embedded in cryogenic Ta. The thin Ta film formed part of a high-resolution superconducting tunnel junction (STJ) radiation detector that was used to identify the signals from different decay channels. The measured $L/K$ capture ratio of 0.070(7) is significantly larger than the only previous measurement of this quantity and the theoretical predictions that include in-medium effects. This result brings into question the accuracy of the extrapolated $L/K$ ratio currently used in calculations of the $^7$Be destruction rate in astrophysical environments relevant to solar and galactic neutrino modeling, and the cosmological lithium problem. This Letter presents the first experiment that uses STJs for nuclear-recoil detection, opening a new experimental avenue for low-energy precision measurements with rare isotopes.