Of course, properties of v µ and v τ cannot be examined by β-spectroscopy since the β-decay energies are not sufficient to create charged μ or τ leptons born together with these neutrinos in the weak interactions. Later on, three kinds (or flavors) of neutrinos were discovered, the electron neutrino v e, the muon neutrino v µ and the tau neutrino v τ. This was a strong, though indirect, argument for the existence of the neutrino. The Fermi theory of β-decay, incorporating the Pauli neutrino and assuming a new type of particle interaction (the weak interaction), predicted the β-spectrum shape that agreed with the experiment. An unexpected shape of measured β-spectra led Pauli to the concept of a new fundamental particle, the neutrino (in addition to the then known electron and proton), saving the law of energy conservation in nuclear β-decay. Β-ray spectroscopy is a powerful tool of neutrino physics. We also pay attention to new experimental approaches and searches for hypothetical sterile neutrinos. We describe important steps in the development of radioactive sources and electron spectrometers, and recapitulate the lessons from now-disproved claims for the neutrino mass of 30 eV and the 17 keV neutrino with an admixture larger than 0.03%. In this review, we summarize the experience of two generations of β-ray spectroscopists who improved the upper limit of m( v e) by three orders of magnitude. The analyses of measured tritium β-spectra provide an upper limit for the effective electron neutrino mass m( v e) < 2 eV. The searches for the yet unobserved 0νββ decay result in an effective neutrino mass m ββ < (0.2 ‒ 0.7) eV. Oscillation experiments have proven that at least one of the neutrino mass states has m i > 0.05 eV while various interpretations of cosmological observations yielded an upper limit for the sum of neutrino masses ∑ m i < (0.14 ‒ 1.7) eV. Although neutrinos are probably the most abundant fermions of the universe their mass is not yet known.
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