Navigating the pitfalls of relic neutrino detection

Beta-spectrum of radioactive atoms was long ago predicted to bear an imprint the cosmic neutrino background ($\mathrm{C}\ensuremath{\nu}\mathrm{B}$) [S. Weinberg, Phys. Rev. 128, 1457 (1962)]. Over years, it has been recognized that best chance achieving signal-to-noise ratio required for observation this effect lies with solid-state designs [E. Baracchini et al., arXiv:1808.01892.]. Here we bring fore a fundamental quantum limitation on type beta-decayer can be used in such design. We derive simple usability criterion and show $^{3}\mathrm{H}$, which is most popular choice, fails meet it. provide list potentially suitable isotopes discuss why their use $\mathrm{C}\ensuremath{\nu}\mathrm{B}$ detection requires further research.