We introduce a new coupling potential to explain the experimental data for
the C-12+(24)Ma system at numerous energies in a laboratory system from 16.
0 MeV to 24.0 MeV. This,new coupled-channels based approach involves replac
ing the usual first derivative coupling potential by a new, second-derivati
ve coupling potential. This paper first shows and discusses the limitation
of the standard coupled-channels theory in the case where one of the nuclei
in the reaction is strongly deformed. Then, this new approach is shown to
improve consistently the agreement with the experimental data and has made
major improvement on all the previous coupled-channels calculations for thi
s system.