Weak nuclear decays deep-underground as a probe of axion dark matter

We investigate the time modulation of weak nuclear decays as a method to probe axion dark matter. To this end, we develop a theoretical framework to compute the θ dependence of weak nuclear decays, including electron capture and β decay, which enables us to predict the time variation of weak radioactivity in response to an oscillating axion dark matter background. As an application, we recast old datasets, from the weak nuclear decays of K40 and Cs137 taken at the underground Gran Sasso Laboratory, in order to set constraints on the axion decay constant, specifically in the axion mass range from few 10-23 up to 10-19 eV. We finally propose a new measurement at the Gran Sasso Laboratory, based on the weak nuclear decay of K40 via electron capture, in order to explore even shorter timescales, thus reaching sensitivities to axion masses up to 10-9 eV.