  We introduce a new coupling potential to explain the experimental data for
the $^{12}$C+$^{24}$Mg system at numerous energies in the laboratory system
from 16.0 MeV to 24.0 MeV. This new coupled-channels based approach involves
replacing the usual first derivative coupling potential by a new,
second-derivative 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 this
system.
