Improved description of the $2\nu\beta\beta$-decay and a possibility to determine the effective axial-vector coupling constant

TL;DR

This paper improves the theoretical formalism for calculating two-neutrino double-beta decay rates by including energy dependence in denominators, leading to more accurate predictions and a new method to determine the effective axial-vector coupling constant.

Contribution

It introduces an enhanced formalism for $2 uetaeta$-decay rate calculation that accounts for energy denominator dependence and proposes a novel approach to determine $g^{ m eff}_{ m A}$.

Findings

Revised decay rate depends on additional phase-space factors.

Correction terms slightly suppress the decay background.

New method to estimate the effective axial-vector coupling constant.

Abstract

An improved formalism of the two-neutrino double-beta decay ($2\nu\beta\beta$-decay) rate is presented, which takes into account the dependence of energy denominators on lepton energies via the Taylor expansion. Till now, only the leading term in this expansion has been considered. The revised $2\nu\beta\beta$-decay rate and differential characteristics depend on additional phase-space factors weighted by the ratios of $2\nu\beta\beta$-decay nuclear matrix elements with different powers of the energy denominator. For nuclei of experimental interest all phase-space factors are calculated by using exact Dirac wave functions with finite nuclear size and electron screening. For isotopes with measured $2\nu\beta\beta$-decay half-life the involved nuclear matrix elements are determined within the quasiparticle random phase approximation with partial isospin restoration. The importance of correction terms to the $2\nu\beta\beta$-decay rate due to Taylor expansion is established and the modification of shape of single and summed electron energy distributions is discussed. It is found that the improved calculation of the $2\nu\beta\beta$-decay predicts slightly suppressed $2\nu\beta\beta$-decay background to the neutrinoless double-beta decay signal. Further, a novel approach to determine the value of effective weak-coupling constant in nuclear medium $g^{\rm eff}_{\rm A}$ is proposed.