Semi-empirical formula for two-neutrino double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay

We propose a semi-empirical formula (SEF) for calculating the nuclear matrix elements (NMEs) for two-neutrino double-\ensuremath{\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.