  Recoilless resonant capture of monoenergetic electron antineutrinos
(Moessbauer antineutrinos) emitted in bound-state beta-decay in the system 3H -
3He is discussed. The recoilfree fraction including a possible phonon
excitation due to local lattice expansion and contraction at the time of the
nuclear transition, homogeneous and inhomogeneous line broadening, and the
relativistic second-order Doppler effect are considered. It is demonstrated
that homogeneous line broadening is essential due to stochastic magnetic
relaxation processes in a metallic lattice. Inhomogeneous line broadening plays
an equally important role. An essential issue which has been overlooked up to
now, is an energy shift of the resonance line due to the direct influence of
the binding energies of the 3H and 3He atoms in the lattice on the energy of
the electron antineutrinos. This energy shift as well as the second-order
Doppler shift exhibit variations in a non-perfect (inhomogeneous) lattice and
may seriously jeopardize the observation of Moessbauer antineutrinos. If
successful in spite of these enormous difficulties, Moessbauer antineutrino
experiments could be used to gain new and deep insights into the nature of
neutrino oscillations, determine the neutrino mass hierarchy as well as up to
now unknown oscillation parameters, search for sterile neutrinos, and measure
the gravitational redshift of electron antineutrinos in the field of the Earth.
