# Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double-$\beta$ and $\beta$ decays

## TL;DR

The paper refines a method to accurately determine nuclear matrix elements for neutrinoless double-beta decay, reducing uncertainties in key parameters, and applies it to specific isotopes with mixed success.

## Contribution

It introduces a new approach to precisely determine the isoscalar pairing interaction and axial-vector coupling, improving the reliability of double-beta decay calculations.

## Key findings

- Successful application to $^{136}$Xe with self-check validation.
- Inability to accurately predict for $^{130}$Te.
- Satisfactory results for $eta$ decay of $^{138}$Xe.

## Abstract

We have proposed in a series of previous papers a method to determine the effective axial-vector current coupling and the strength of the isoscalar proton-neutron pairing interaction for calculating the nuclear matrix elements of the neutrinoless double-$\beta$ decay by the quasiparticle random-phase approximation. The combination of these two parameters have had an uncertainty in this approach, but now this uncertainty is removed. In this paper, we apply our method to the neutrinoless double-$\beta$ decays of $^{136}$Xe and $^{130}$Te and predict the nuclear matrix elements and reduced half-lives. Our calculation is tested first by a self-check method using the two-neutrino double-$\beta$ decay, and this test ensures the application of our method to $^{136}$Xe. It turns out, however, that our method is not successful in $^{130}$Te. Further test is made for our calculation of the $\beta$ decay of $^{138}$Xe, and a satisfactory result is obtained.