Inelastic nuclear scattering from neutrinos and dark matter

Neutrinos with energy of order 10~MeV, such as from pion decay-at-rest sources, are an invaluable tool for studying low-energy neutrino interactions with nuclei -- previously enabling the first measurement of coherent elastic neutrino-nucleus scattering. Beyond elastic scattering, neutrinos and dark matter in this energy range also excite nuclei to its low-lying nuclear states, providing an additional physics channel. Here, we consider neutral-current inelastic neutrino-nucleus and dark matter(DM)-nucleus scattering off $^{40}$Ar, $^{133}$Cs, and $^{127}$I nuclei that are relevant to a number of low-threshold neutrino experiments at pion decay-at-rest facilities. We carry out large scale nuclear shell model calculations of the inelastic cross sections considering the full set of electroweak multipole operators. Our results demonstrate that Gamow-Teller transitions provide the dominant contribution to the cross section and that the long-wavelength limit provides a reasonable approximation to the total cross section for neutrino sources. We show that future experiments will be sensitive to this channel and thus these results provide additional neutrino and DM scattering channels to explore at pion decay-at-rest facilities.