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

The nuclear matrix elements $M^{0ν}$ of the neutrinoless double beta decay ($0νββ$) 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 $2νββ$ decay rate is correctly reproduced, the resulting $M^{0ν}$ 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 $M^{0ν}$ within these methods is eliminated.