  In this work we obtain the analytical expressions for the boundaries of the
charged current quasi-elastic double differential cross section in terms of
dimensionless energy and momentum transfers, for the Relativistic Fermi Gas
(RFG) and the Super-Scaling approach with relativistic effective mass (SuSAM*)
models, within the scaling formalism. In addition, this new double differential
cross section in the scaling formalism has very good properties to be
implemented in the Monte Carlo (MC) neutrino event generator, particularly
because its peak is almost flat with the (anti)neutrino energy. This makes it
especially well-suited for the event generation by the acceptance-rejection
method usually used in the neutrino generators. Finally, we analyze the total
charged current quasi-elastic (CCQE) cross section $\sigma(E_{\nu})$ for both
models and attribute the enhancement observed in the SuSAM* total cross section
to the high-momentum components which are present, in a phenomenological way,
in its scaling function, while these are absent in the RFG model.
