Gamow-Teller and double-beta decays of heavy nuclei within an effective theory

We study $\beta$ decays within an effective theory that treats nuclei as a spherical collective core with an even number of neutrons and protons that can couple to an additional neutron and/or proton. First we explore Gamow-Teller $\beta$ decays of parent odd-odd nuclei into low-lying ground-, one-, and two-phonon states of the daughter even-even system. The low-energy constants of the effective theory are adjusted to data on $\beta$ decays to ground states or Gamow-Teller strengths. The corresponding theoretical uncertainty is estimated based on the power counting of the effective theory. For a variety of medium-mass and heavy isotopes the theoretical matrix elements are in good agreement with experiment within the theoretical uncertainties. We then study the two-neutrino double-$\beta$ decay into ground and excited states. The results are remarkably consistent with experiment within theoretical uncertainties, without the necessity to adjust any low-energy constants.