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Double beta decay of '2'Te has been confirmed and the ratio of half-lives for pp decay of " Te and Te has been precisely determined as Tl&2/T',~&=(3.52+0. 11)X10 by ion-counting mass spectrometry of Xe in ancient Te ores, using techniques that reduce interferences due to trapped Xe. We have also detected excesses of ' Xe originating in high energy reactions of cosmic ray muons and their secondaries on Te; such reactions make minor contributions to the measured ' Xe excesses in the Te ores. The Xe measurements, combined with common Pb dating of the ores, yield a ' Te half-life of (2.7+0. 1)X 10 ' yr and thus a ' Te half-life of (7.7+0.4) X 10 yr the longest radioactive decay lifetime measured to date. These results give limits on the effective Majorana mass of the neutrino ( & 1.1 -1.5 eV) and right-handed currents (~(g )~( 5.3 X 10 ') comparable to the best obtained from direct neutrinoless PP-decay searches. They also imply new limits on unconventional Majorons not constrained by measurements of the Z decay width. PACS number(s): 23.40.8w, 14.60.Gh, 14.80.Gt, 27.60.+j PRECISE DETERMINATION OF RELATIVE AND ABSOLUTE. . . 807 T0( m ) to T0 ( m ), where ( m ) is the effective Majorana mass of the neutrino [4,5]. This implies that the relative contribution of Ov /3P decay to the ' Te decay (TQ =0.87 MeV) is much larger than that for ' Te (T0 =2.53 MeV) for values of ( m ) near the current limits of a few eV. The experimental advantage of the Te system is that both of the daughters of the Te PP decay, Xe and ' Xe, are noble gases which can be easily extracted from Te ores. Their ratio, ' Xe/' Xe, is directly proportional to the ratio of decay rates I' /I', and can be determined with relatively high precision by noble-gas mass spectrometry, thus eliminating many sources of systematic error. These advantages provided by the Te system have prompted many groups to study it, and although the decay of ' Te is well established, there has been a longstanding controversy over whether PP decay of ' Te has actually been observed. Several studies by the University