  Any discovery of `new physics' in the neutrino sector first requires a
precise prediction of the expected Standard Model cross section. Currently,
Coherent Elastic neutrino-Nucleus Scattering (CEvNS) experiments are statistics
limited. However, as new and future experiments scale up, it will be necessary
to improve the theoretical predictions. Here we review the calculation of the
CEvNS cross section in a consistent theory of hadronic currents and compute the
relevant nuclear form factors using the nuclear shell model. The uncertainty on
the form factors is explored by repeating the calculation for various shell
model interactions and with Skyme-Hartree-Fock evaluations of the Weak-charge
radii. We then refine the Standard Model predictions for the recent
experimental results of the COHERENT experiment. We find that our cross
sections are in good agreement with previous predictions, but with
significantly smaller uncertainties - by up to a factor of 10. Near-future
CEvNS experiments will meaningfully benefit from improved predictions through
an increased sensitivity to new-physics signals.
