The nuclei ${}^{151}\mathrm{Sm}$ and ${}^{171}\mathrm{Tm}$ have been identified as attractive candidates for the detection of the cosmic neutrino background. Both isotopes undergo first-forbidden nonunique beta decays, which inhibits a prediction of their spectral shape using symmetries alone, and this has, so far, obstructed a definitive prediction of their neutrino capture cross sections. In this work we point out that for both elements the so-called $\xi$ approximation is applicable and this effectively limits the spectral shape to a deviation of at most $1\%$ from the one that would arise if beta decays were of the allowed type. Using measured half-lives we extract the relevant nuclear matrix element and predict the neutrino capture cross sections for both isotopes at the $1\%$ level, accounting for a number of relevant effects including radiative corrections and the finite size of the nuclei. We obtained $(1.12\pm 0.01)\times {10}^{-46}{\mathrm{cm}}^2$ for ${}^{171}\mathrm{Tm}$ and $(4.77\pm 0.01)\times {10}^{-48}{\mathrm{cm}}^2$ for ${}^{151}\mathrm{Sm}$. This method is robust as it does not rely on the data points near the endpoint of the beta spectrum, which may be contaminated by atomic physics effects, namely shakeup and shakeoff. Finally, we calculate the target mass which is necessary for cosmic neutrino discovery and discuss several bottlenecks and respective solutions associated to the experimental program. We conclude that the detection of cosmic neutrino background by neutrino capture on ${}^{151}\mathrm{Sm}$ and ${}^{171}\mathrm{Tm}$ is achievable and free from theoretical limitations but still subject to technical issues that should be further investigated by the experimentalists in the context of the proposed PTOLEMY project.

• Received 4 February 2022
• Accepted 31 March 2022

DOI:https://doi.org/10.1103/PhysRevC.105.045501

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Published by the American Physical Society