  Both neutrino and antineutrino charged-current quasi-elastic scattering on a
carbon target are studied to investigate the nuclear effect on the
determination of the axial form factor F_A(Q^2). A method for extraction of
  F_A(Q^2) from the flux-integrated $d\sigma/dQ^2$ cross section of
(anti)neutrino scattering on nuclei is presented. Data from the MiniBooNE
experiment are analyzed in the relativistic distorted-wave impulse
approximation, Fermi gas model, and in the Fermi gas model with enhancements in
the transverse cross section. We found that the values of the axial form
factor, extracted in the impulse approximation and predicted by the dipole
approximation with the axial mass M_A~1.37 GeV are in good agreement. On the
other hand, the Q^2-dependence of F_A extracted in the approach with the
transverse enhancement is found to differ significantly from the dipole
approximation.
