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

Abstract

In this work we present the first beyond closure calculation for the neutrinoless double beta decay (0νββ) 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 gpp plays an important role for the calculations and if quenching is included, suppression for the transition matrix element M λ 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.