Basic aspects of phononless resonant capture of monoenergetic electron antineutrinos (Moessbauer antineutrinos) emitted in boundstate beta-decay in the 3H - 3He system are considered. It is shown that stochastic magnetic relaxation phenomena as well as the direct influence of solid-state effects on the energy of the electron antineutrino will cause line broadening by a factor of more than 10^(13). Lattice expansion and contraction after the transformation of the nucleus will drastically reduce the probability for phononless transitions. Thus, the observation of Moessbauer electron antineutrinos of the 3H - 3He system will most probably be unsuccessful. As a possible alternative, the Rare-Earth system 163Ho - 163Dy is briefly discussed.
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