A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay

We propose a semi-empirical formula (SEF) for calculating the nuclear matrix elements (NMEs) for two-neutrino double-beta decay. The SEF’s dependence on the proton and neutron numbers, the pairing, isospin, and deformation properties of the initial and final nuclei is inspired by the insights offered by nuclear many-body methods and trends in experimental data. Compared with the previous phenomenological and nuclear models, the SEF yields the best agreement with the experimental NMEs. Its stability and predictive power are cross-validated, and predictions are provided for nuclear systems of experimental interest.

💡 Research Summary

The paper introduces a semi‑empirical formula (SEF) designed to predict the nuclear matrix elements (NMEs) governing two‑neutrino double‑beta (2νββ) decay. The authors begin by emphasizing the importance of 2νββ as the only Standard‑Model‑allowed double‑beta process that has been directly observed in nine nuclei, and they note the persistent discrepancy between experimental NMEs and theoretical calculations based on a variety of many‑body approaches (pn‑QRPA, nuclear shell model, interacting boson model, projected Hartree‑Fock‑Bogoliubov, etc.). Existing models either require nucleus‑by‑nucleus parameter tuning or fail to capture systematic trends such as the impact of nuclear deformation, pairing, and isospin.

In the “Current State” section, the decay rate is expressed as
( (T_{1/2}^{2\nu})^{-1}=G_{2\nu},|M_{2\nu}|^{2} ),
where the phase‑space factor (G_{2\nu}) is taken from state‑of‑the‑art relativistic DFT calculations. The matrix element (M_{2\nu}) is dominated by the Gamow‑Teller part, with the Fermi contribution suppressed by isospin symmetry. The authors review the strengths and weaknesses of each theoretical framework, highlighting that deformation mismatches between parent and daughter nuclei, as well as the magnitude of proton‑neutron pairing gaps, are decisive for the size of the NME.

Motivated by these observations, the SEF is proposed in the following compact form:

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