  Neutrino-nucleus coherent elastic scattering provides a theoretically
appealing way to measure the neutron part of nuclear form factors. Using an
expansion of form factors into moments, we show that neutrinos from stopped
pions can probe not only the second moment of the form factor (the neutron
radius) but also the fourth moment. Using simple Monte Carlo techniques for
argon, germanium, and xenon detectors of 3.5 tonnes, 1.5 tonnes, and 300 kg,
respectively, we show that the neutron radii can be found with an uncertainty
of a few percent when near a neutrino flux of $3\times10^{7}$
neutrinos/cm$^{2}$/s. If the normalization of the neutrino flux is known
independently, one can determine the moments accurately enough to discriminate
among the predictions of various nuclear energy functionals.
