  We analyze the possibility of detection of cosmological relic neutrinos via
neutrino capture on beta decaying nuclei. This reaction has no threshold in
neutrino energy, which is crucial for searching for relic neutrinos possessing
very low energies. We focus on tritium (3H) and rhenium (187Re) beta
radioactive isotopes to be used in KATRIN and MARE experiments dedicated to
measurement of the electron neutrino mass at sub-eV scale. We examine these
experiments from the viewpoint of searching for the cosmological neutrinos via
neutrino capture. We conclude that even with possible gravitational clustering
of relic neutrinos the prospects for their detection in these and other similar
experiments are not optimistic. Nevertheless KATRIN and MARE experiments could
establish some usefull constraints on density of relic neutrinos.
