The possible test of the calculations of nuclear matrix elements of the   $(\beta \beta)_{0\nu}$-decay
  The existing calculations of the nuclear matrix elements of the neutrinoless double $\beta$-decay differ by about a factor three. This uncertainty prevents quantitative interpretation of the results of experiments searching for this process. We suggest here that the observation of the neutrinoless double $\beta$-decay of {\em several} nuclei could allow to test calculations of the nuclear matrix elements through the comparison of the ratios of the calculated lifetimes with experimental data. It is shown that the ratio of the lifetimes is very sensitive to different models. 
S. M. Bilenky and J. A. Grifols