Nuclear Recoil-Gamma Coincidence Spectroscopy in 7Be EC Decay using Superconducting Sensors*

Precision measurements of the $^7$Li recoil energy from electron capture (EC) decay of $^7$Be in superconducting tunnel junction (STJ) sensors currently provide the most stringent limits on sub-MeV heavy neutrino mass states, and access to the quantum nature of the neutrino. However, in 10\% of $^7$Be EC decays, a 478 keV excited state in $^7$Li is populated with a half-life of 74 fs. Using an array of high-efficiency NaI detectors surrounding the low-temperature stage of an adiabatic demagnetization refrigerator, we have measured the 478 keV $\gamma$-ray in coincidence with the $\sim$11~eV $^7$Li nuclear recoil signal in the STJs. Given that the excited-state half-life is of the same order as the slow-down time of the recoil in the material, we have been able to extract the shape of the nuclear recoil Doppler profile. The high precision of the measurement enables testing molecular dynamics simulations and conventional models of nuclear slow-down at $\lesssim$ 11 eV, as well as characterizing the dominant spectral background in the BeEST experiment. This talk will present the first direct nuclear recoil-$\gamma$ coincidence measurement in EC decay and analysis of the stopping power profile.