  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.
