Uncertainty in the0νββdecay nuclear matrix elements

The nuclear matrix elements $M^{0\nu }$ of the neutrinoless double-beta decay $\left(0\nu \beta \beta \right)$ are evaluated for ${}^{76}\mathrm{Ge},{}^{100}\mathrm{Mo},{}^{130}\mathrm{Te},$ and ${}^{136}\mathrm{Xe}$ within the renormalized quasiparticle random phase approximation (RQRPA) and the simple QRPA. Three sets of single particle level schemes are used, ranging in size from 9 to 23 orbits. When the strength of the particle-particle interaction is adjusted so that the $2\nu \beta \beta$ decay rate is correctly reproduced, the resulting $M^{0\nu }$ values become essentially independent of the size of the basis, and of the form of different realistic nucleon-nucleon potentials. Thus, one of the main reasons for variability of the calculated $M^{0\nu }$ within these methods is eliminated.