  Neutrino-nucleus $\nu A\to \nu A$ and antineutrino-nucleus $\bar\nu A\to
\bar\nu A$ interactions, when the nucleus conserves its integrity, are
discussed with coherent (elastic) and incoherent (inelastic) scattering regimes
taken into account. In the first regime the nucleus remains in the same quantum
state after the scattering and the cross-section depends on the quadratic
number of nucleons. In the second regime the nucleus changes its quantum state
and the cross-section has an essentially linear dependence on the number of
nucleons. The coherent and incoherent cross-sections are driven by a nuclear
nucleon form-factor squared $|F|^2$ term and a $(1-|F|^2)$ term, respectively.
One has a smooth transition between the regimes of coherent and incoherent
(anti)neutrino-nucleus scattering. Due to the neutral current nature these
elastic and inelastic processes are indistinguishable if the nucleus recoil
energy is only observed. One way to separate the coherent signal from the
incoherent one is to register $\gamma$ quanta from deexcitation of the nucleus
excited during the incoherent scattering. Another way is to use a very
low-energy threshold detector and collect data at very low recoil energies,
where the incoherent scattering is vanishingly small. In particular, for
${}^{133}\text{Cs}$ and neutrino energies of 30--50 MeV the incoherent
cross-section is about 15-20\% of the coherent one. Therefore, the COHERENT
experiment (with ${}^{133}\text{Cs}$) has measured the coherent elastic
neutrino nucleus scattering (CE$\nu$NS) with the inelastic admixture at a level
of 15-20\%, if the excitation $\gamma$ quantum escapes its detection.
