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

TL;DR

This paper develops an effective theory to analyze Gamow-Teller and double-beta decays in heavy nuclei, achieving good agreement with experimental data and providing a new framework for understanding nuclear decay processes.

Contribution

It introduces a novel effective theory approach for heavy nuclei decays, accurately predicting decay matrix elements without extensive parameter fitting.

Findings

Theoretical matrix elements agree with experimental data within uncertainties.

The approach accurately predicts double-beta decay rates without adjusting low-energy constants.

Uncertainty estimates are systematically derived from effective theory power counting.

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.