  In this work we extend a previously derived $n$- $^9$Be optical potential up
to 500 MeV and apply it to the system $n$- $^{12}$C, finding excellent results
for the energy dependence of the total cross sections. Results obtained with a
standard optical model calculation are compared to those from the eikonal
formalism in order to asses the accuracy of the latter as a function of the
nucleon incident energy. For comparison, single folded (s.f.) nucleon-target
potentials are also obtained using $^{12}$C densities from different models.
These potentials are sensitive to the density used and none of them reproduce
the characteristics of the phenomenological potential nor the cross section
results. We then calculate nucleus-nucleus ($NN$) potentials and total reaction
cross sections for some "normal" and exotic projectile nuclei on $ ^ {12} $C
within the eikonal formalism. We find that single folded (S.F.)
projectile-target imaginary potentials and double folded (D.F.) potentials can
produce similar energy dependence of the reaction cross sections but the S.F.
results agree better with experimental data provided the radius parameter of
the phenomenological $n$-target potential is allowed to be energy dependent. We
conclude that the results previously obtained for a $^9$Be target are quite
general, at least for light systems, and that a S.F. $NN$ potential built on a
phenomenological nN potential can constitute an interesting and useful
alternative to D.F. potentials.
