Coherent elastic neutrino-nucleus scattering (CEvNS) can be used to determine
the neutron part of nuclear form factors, unlocking intrinsic properties of
nuclear structure. In contrast with other such methods, CEvNS is free from both
strong interaction effects and Coulomb distortions. We propose precision
measurements of CEvNS with an upcoming accelerator facility and determine the
corresponding requirements for such a neutrino detector. We find that most
significant backgrounds come from fast neutrons, induced by cosmogenic muons or
from the pion decays at rest in the target station. With ton-scale liquid noble
gas detectors, we will not only achieve percent level precision in the
measurement of neutron radii but also clarify contributions of higher-order
moments to nuclear form factors.Comment: 19 pages, 8 figures. Match the published version and include a
discussion of the detector's energy threshold on the precision of form factor
measurements in the appendi