  Neutral current quasielastic (anti)neutrino scattering cross sections on a
$^{12}$C target are analyzed using a realistic spectral function $S(p,E)$ that
gives a scaling function in accordance with the ($e,e'$) scattering data. The
spectral function accounts for the nucleon-nucleon (NN) correlations by using
natural orbitals (NOs) from the Jastrow correlation method and has a realistic
energy dependence. The standard value of the axial mass $M_A= 1.032$ GeV is
used in all calculations. The role of the final-state interaction (FSI) on the
spectral and scaling functions, as well as on the cross sections is accounted
for. A comparison of the calculations with the empirical data of the MiniBooNE
and BNL experiments is performed. Our results are analyzed in comparison with
those when NN correlations are not included, and also with results from other
theoretical approaches, such as the relativistic Fermi gas (RFG), the
relativistic mean field (RMF), the relativistic Green's function (RGF), as well
as with the SuperScaling Approach (SuSA) based on the analysis of quasielastic
electron scattering.
