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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 ofa high-resolution superconducting tunnel junction (STJ) radiation detector thatwas 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 previousmeasurement of this quantity and the theoretical predictions that includein-medium effects. This value is a uniquely sensitive probe of the 1s and 2sorbital overlaps with the nucleus, and is of relevance to nuclear and atomicphysics, 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 withrare isotopes.

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