  We discuss the effects of neutrino mixing and the neutrino mass hierarchy
when considering the capture of the cosmic neutrino background (CNB) on
radioactive nuclei. The implications of mixing and hierarchy at future
generations of tritium decay experiments are considered. We find that the CNB
should be detectable at these experiments provided that the resolution for the
kinetic energy of the outgoing electron can be pushed to a few 0.01 eV for the
scenario with inverted neutrino mass hierarchy, about an order of magnitude
better than that of the upcoming KATRIN experiment. Another order of magnitude
improvement is needed in the case of normal neutrino mass hierarchy. We also
note that mixing effects generally make the prospects for CNB detection worse
due to an increased maximum energy of the normal beta decay background.
