# Determination of Strength of Isoscalar Pairing Interaction by a Mathematical Identity in QRPA

## TL;DR

This paper introduces a novel mathematical method within QRPA to accurately determine the strength of isoscalar proton-neutron pairing interactions, with applications to neutrinoless double-beta decay in specific nuclei.

## Contribution

A new approach using a mathematical identity in QRPA to determine isoscalar pairing strength, improving predictions for neutrinoless double-beta decay.

## Key findings

- Calculated reduced half-life for $^{48}$Ca
- Demonstrated method's applicability to nuclei relevant for neutrinoless double-beta decay
- Provided insights into pairing interactions affecting neutrino mass estimates

## Abstract

I propose a new method to determine the strength of the isoscalar proton-neutron pairing interaction by a mathematical identity derived in the quasiparticle random-phase approximation. This method is applied for a few nuclei possibly having the neutrinoless double-$\beta$ decay. Reduced half-life, the theoretical quantity necessary for determining the effective neutrino mass, is calculated for $^{48}$Ca.