Charged current cross section for massive cosmological neutrinos impinging on radioactive nuclei

We discuss the cross section formula for both massless and massive neutrinos on stable and radioactive nuclei. The latter could be of interest for the detection of cosmological neutrinos whose observation is one of the main challenges of modern cosmology. We analyse the signal-to-background ratio as a function of the ratio m(v)/Delta, i.e. the neutrino mass over the detector resolution and show that an energy resolution Delta <= 0.5 eV would be required for sub-eV neutrino masses, independently of the gravitational neutrino clustering. Finally, we mention the non-resonant character of neutrino capture on radioactive nuclei.