Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory

TL;DR

This paper develops an efficient computational approach within nuclear density functional theory to accurately calculate two-neutrino double-beta decay matrix elements across many nuclei, aiding in the understanding of neutrinoless double-beta decay.

Contribution

It introduces a double contour integration method within the finite amplitude approach to evaluate $2 uetaeta$ nuclear matrix elements in large model spaces without truncation, using globally fitted functionals.

Findings

Reproduces experimental matrix elements without fitting to half-lives.

Provides predictions for 27 nuclei with unmeasured half-lives.

Demonstrates the method's efficiency and accuracy in large-scale calculations.

Abstract

Two-neutrino double-beta ($2\nu\beta\beta$) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine $2\nu\beta\beta$ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. We work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to $2\nu\beta\beta$ half-lives themselves, to evaluate the $2\nu\beta\beta$ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.