  The neutral current elastic scattering of neutrinos on Carbon and $CH_2$
targets is computed using the relativistic distorted-wave impulse approximation
with relativistic optical potential. Results for exclusive and inclusive
neutrino reactions on ${}^{12}$C target are presented. We show that the nuclear
effects on the shape of four-momentum transferred squared distribution
$d\sigma/dQ^2_{QE}$ in neutrino neutral-current and charged-current
quasi-elastic scattering are similar. We also calculate flux-averaged neutral
current elastic differential cross section $d\sigma/dQ^2_{QE}$ for neutrino
scattering from $CH_2$, as well as, the neutral-current to charged-current
cross section ratio as functions of $Q^2_{QE}$. The value of axial mass $M_A$
is extracted from a fit of $d\sigma/dQ^2_{QE}$ cross section measured in
MiniBooNE experiment. The extracted value of $M_A=1.28\pm 0.05$ GeV is
consistent within errors with the MiniBooNE result. Additionally, for proton
kinetic energies above the Cherenkov threshold, the strange quark contribution
to the neutral current axial vector form factor at $Q^2_{QE}=0$, $\Delta s$,
was extracted from a fit of MiniBoone data for $\nu p \to \nu p$ to $\nu N \to
\nu N$ cross section ratio. This value is found to be $\Delta s=-0.11\pm 0.36$

High Energy Physics - Phenomenology;Nuclear Theory