On the uncertainty in the $0 ubetabeta$ decay nuclear matrix elements

The nuclear matrix elements $M^{0 u}$ of the neutrinoless double beta decay ($0 ubetabeta$) are evaluated for $^{76}$Ge,$^{100}$Mo, $^{130}$Te, and $^{136}$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 $2 ubetabeta$ decay rate is correctly reproduced, the resulting $M^{0 u}$ values become essentially independent on the size of the basis, and on the form of different realistic nucleon-nucleon potentials. Thus, one of the main reasons for variability of the calculated $M^{0 u}$ within these methods is eliminated.