Prospects for precision CE$ν$NS measurements with electron-capture neutrinos and lithium-based bolometers

We evaluate the feasibility of high-precision coherent elastic neutrino-nucleus scattering measurements exploiting mono-energetic neutrinos produced by electron-capture (EC) decays of intense radioactive sources, such as $^{51}$Cr or $^{37}$Ar. To fully exploit the high neutrino flux achievable with EC sources, and accounting for the low energy of EC neutrinos, we evaluate the sensitivity of a compact array of bolometric detectors with absorbers based on light elements, such as lithium, oxygen and fluorine. With 1 kg of LiF detectors, source activities of $\sim10^{17}$ Bq, and assuming an energy threshold of 20 eV, we expect to achieve a $\sim 3\%$ precision on the determination of the neutrino flux with 90 days of measurement. Such a measurement would represent a test of the gallium neutrino anomaly, and could disentangle nuclear effects on gallium from the misevaluation of the EC source activity or short-baseline neutrino oscillations.