  The M\"ossbauer technique is proposed as an alternative experimental
procedure to be used in the detection of Coherent Elastic $\nu$-Nucleus
Scattering (CENNS). The $Z_{0}$-boson exchange is considered as a perturbation
on the nuclear mean-field potential with a change in the valence neutron
quantum states in the $^{57}Fe$ nucleus of the M\"ossbauer detector sample.
This nuclei is a typical isotope used in M\"ossbauer spectroscopy. Perturbed
level of the valence neutron accommodates the transferred energy, modifying the
location of the isometric peak of the M\"ossbauer electromagnetic resonance. We
calculate the isometric shift correction due CENNS and show that this quantity
is able to be detected with enough precision. Therefore, the difference between
the M\"ossbauer isometric shift in the presence of a reactor-neutrino beam and
without the neutrinos flux is pointed out as a figure of merit to manifest
CENNS. In this work, we show that the CENNS correction of the Isomeric Shift is
of $\approx 10^{-7}$eV, which is greater than the $10^{-10}$eV resolution of
the technique.
