  This letter introduces a new coupling potential to explain the experimental
data over wide energy ranges for a number of systems. Within the
coupled-channels formalism, this letter first shows the limitations of the
standard coupled-channels theory in the case where one of the nuclei in the
reaction is strongly deformed and then, demonstrates that a global solution to
the problems of light heavy-ion reactions such as $^{12}$C+$^{12}$C,
$^{16}$O+$^{28}$Si and $^{12}$C+$^{24}$Mg can be found using a new
second-derivative coupling potential in the coupled-channels formalism. This
new approach consistently improves the agreement with the experimental data for
the elastic and inelastic scattering data as well as for their excitation
functions using constant or slightly energy-dependent parameters.
