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

Abstract

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.

17 pages, 5 figures, results extended to two-neutrino double beta-minus decays and two-neutrino double electron-capture decays to excited 2+ states, matches published version

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• Neutrinoless double-beta decay from an effective field theory for heavy nuclei
• Nuclear matrix elements for neutrinoless double beta decays and spin-dipole giant resonances
• Two-neutrino double-beta decay matrix elements based on relativistic nuclear energy density functional
• The Majorana Demonstrator's Search for Double-Beta Decay of ${}^{76}$Ge to Excited States of ${}^{76}$Se
• Two-neutrino $\beta \beta$ decay of ${}^{136}$Xe to the first excited $0^{+}$ state in ${}^{136}$Ba
• Radiative and exchange corrections for two-neutrino double-beta decay
• Final Results of the MAJORANA DEMONSTRATOR's Search for Double-Beta Decay of ${}^{76}$Ge to Excited States of ${}^{76}$Se
• Effective field theories for collective excitations of atomic nuclei
• A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay
• Large-scale shell-model investigation of $2\nu$ECEC in ${}^{132}$Ba and ${}^{78}$Kr