Accurate shell-model nuclear matrix elements for neutrinoless double-beta decay

TL;DR

This paper introduces a new method for accurately calculating nuclear matrix elements for neutrinoless double-beta decay, achieving better than 1% accuracy with convergence properties and optimized closure energies.

Contribution

The authors develop a novel calculation method that ensures convergence and high accuracy for nuclear matrix elements, improving upon previous approaches.

Findings

Matrix elements have perfect convergence with only 100 intermediate states.

The method achieves better than 1% accuracy in calculations.

Optimal closure energies are identified for improved estimates.

Abstract

We investigate a novel method of accurate calculation of the neutrinoless double-$\beta$ decay shell-model nuclear matrix elements for the experimentally relevant case of $^{76}$Ge. We demonstrate that with the new method the nuclear matrix elements have perfect convergence properties and, using only the first 100 intermediate states of each spin, the matrix elements can be calculated with better than 1% accuracy. Based on the analysis of neutrinoless double-beta decays of $^{48}$Ca, $^{82}$Se, and $^{76}$Ge isotopes, we propose a new method to estimate the optimal values of the average closure energies at which the closure approximation gives the most accurate nuclear matrix elements. We also analyze the nuclear matrix elements for the heavy-neutrino-exchange mechanism, and we show that our method can be used to quench contributions from different intermediate spin states.