Corresponding author exist scenarios in which the effective Majorana mass of the electron neutrino could be larger than 0.05 eV. Recent developments in detector technology make the observation of 0 νββ decay at this scale now feasible. For recent comprehensive experimental and theoretical reviews see [4][5][6]. Optimism that a direct observation of 0 νββ decay is possible was greatly enhanced by the observation and measurement of the oscillations of atmospheric neutrinos [7], the confirmation by SuperKamiokande [8] of the deficit of 8 B neutrinos observed by the chlorine experiment [9], the observed deficit of p-p neutrinos by SAGE [10] and GALEX [11], and the results of the SNO experiment [12] that clearly showed that the total flux of 8 B neutrinos from the sun predicted by Bahcall and his coworkers [13] is correct. Finally, the data from the KamLAND