  At energies below the Coulomb barrier, the fusion excitation function for the
$^{12}$C+$^{12}$C system shows prominent fine structures, whereas that for the
$^{12}$C+$^{13}$C system behaves more smoothly as a function of energy. We
demonstrate that these different behaviors can be simultaneously reproduced
using an optical potential in which the strength of the imaginary part is
proportional to the level density of each compound nucleus. We also discuss the
oscillatory behavior of fusion excitation function for these systems observed
at energies above the Coulomb barrier from a view point of quantum mechanical
systems with identical particles.
