  The effects of the nuclear structure uncertainties on the description of
processes induced by coherent scattering of neutrinos on nuclei are
investigated. A reference calculation based on a specific nuclear model is
defined and the cross sections and also the expected number of events produced
by neutrinos generated by the explosion of a supernova in our galaxy, and by a
spallation neutron source are evaluated. By changing the input parameters of
the reference calculation their relevance on cross sections and on the number
of the detected events is estimated. Seven spherical nuclei with different
proton to neutron ratios are considered as possible targets of the neutrinos in
the detector, the lightest being $^{12}$C and the heaviest $^{208}$Pb. The
effects generated by the uncertainties of the nuclear model are much smaller
than those due to the supernova neutrino flux models. This makes the coherent
elastic neutrino-nucleus scattering a reliable tool to investigate the details
of the neutrino sources, the neutrino-nucleus interaction, and, eventually,
also to extract information about neutron distributions in nuclei.
