Examinations of the consistency of the quasiparticle random-phase approximation approach to double-$\beta$ decay of $^{48}$Ca

TL;DR

This paper assesses the consistency of the QRPA method for calculating nuclear matrix elements of double-beta decay in calcium-48, comparing different approaches and experimental data, and finds no fundamental issues with the method.

Contribution

It provides a detailed consistency examination of the QRPA approach for double-beta decay NMEs, including treatment of intermediate states and comparison with experimental charge-exchange data.

Findings

QRPA approach shows no decisive problems.

Neutrinoless double-beta NME is consistent with other QRPA calculations.

Adjusted NME is among the lowest values, close to other QRPA results.

Abstract

The nuclear matrix elements (NMEs) of the neutrinoless and two-neutrino double-$\beta$ decays of $^{48}$Ca are calculated by the quasiparticle random-phase approximation (QRPA) with emphasis on the consistency examinations of this calculation method. The main new examination points are the consistency of two ways to treat the intermediate-state energies in the two-neutrino double-$\beta$ NME and comparison with the experimental charge-exchange strength functions obtained from $^{48}$Ca$(p,n)$ and $^{48}$Ti$(n,p)$ reactions. No decisive problem preventing the QRPA approach is found. The obtained neutrinoless double-$\beta$ NME adjusted by the ratio of the effective and bare axial-vector current couplings is lowest in those calculated by several groups and close to one of the QRPA values obtained by another group.