Basic aspects of phononless resonant capture of monoenergetic electron antineutrinos (Mössbauer antineutrinos) emitted in bound-state \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 \bar  \nu _e will cause line broadening by a factor of more than 10¹³. Lattice expansion and contraction after the transformation of the nucleus will drastically reduce the probability for phononless transitions. Thus, the observation of Mössbauer \bar \nu _e of the ³H–³He system will most probably be unsuccessful. As a possible alternative, the rare-earth system ¹⁶³Ho–¹⁶³Dy is briefly discussed.

PACS numbers: 14.60.Pq, 13.15.+g, 76.80.+y, 76.20.+q