Direct measurement of the $^7$Be $L/K$ capture ratio in Ta-based superconducting tunnel junctions

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 value is a uniquely sensitive probe of the 1s and 2s orbital overlaps with the nucleus, and is of relevance to nuclear and atomic physics, as well as Li production in novae and other astrophysical scenarios. This is the first experiment that uses STJs for nuclear-recoil detection, opening a new experimental avenue for low-energy precision measurements with rare isotopes.