NMEs for $0\hat{I}½{\hat{I}}^2{\hat{I}}^2(0^{+}\to 2^{+})$ of two-nucleon mechanism for ${}^{76}$Ge

Abstract

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ($0\hat{I}½{\hat{I}}^2{\hat{I}}^2$) 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 $M_{\hat{I}}»$ 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.

10 pages, 4 figures