The beta spectrum of tritium has been studied with a pi square root (13)/2-spectrometer. The source consisted of tritium in the atomic form embedded in a metal-dioxide lattice. The measured spectrum was analysed down to 14 keV. All fitting parameters used, in addition to the mass parameter mnu , could be checked by independently determined physical values. No evidence for a non-vanishing antineutrino mass or a mixed state with a heavy antineutrino admixture in the mass region from 0.010 to 4 keV/c2 was found. Typical upper limits for the amplitude were 1.8*10-3 for a 3 keV/c2 and 16*10-3 for a 0.6 keV/c2 heavy neutrino branch at 95% confidence. The value of the electron antineutrino mass was determined to be mnu =15-15+32 eV/c2. The mass difference Delta M(3H-3He) was found to be 18597+or-14 eV/c2. Experimental effects influencing the determination of the rest mass are discussed and considered in the results.
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