NMEs for $0\nu\beta\beta(0^+\rightarrow2^+)$ of two-nucleon mechanism for $^{76}$Ge

TL;DR

This paper presents a novel beyond-closure calculation of neutrinoless double beta decay for $^{76}$Ge to $2^+$ states, revealing larger nuclear matrix elements than previous models, with implications for decay rate predictions.

Contribution

It introduces the first beyond-closure QRPA calculation for $^{76}$Ge $0 uetaeta$ decay to $2^+$ states, improving nuclear matrix element estimates.

Findings

Nuclear matrix elements are about ten times larger than previous results.

Including quenching suppresses the transition matrix elements.

The isospin symmetry restored QRPA with realistic force is effective.

Abstract

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ($0\nu\beta\beta$) of $^{76}$Ge to the first $2^+$ states of $^{76}$Se. The isospin symmetry restored Quasi-particle random phase approximation (QRPA) method with the CD-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the two nucleon mechanism nuclear matrix elements, and estimate the uncertainties from the nuclear many-body calculations. We find $g_{pp}$ plays an important role for the calculations and if quenching is included, suppression for the transition matrix element $M_{\lambda}$ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hatree-Fock-Boglyubov results with the closure approximation.