  In a theoretical approach, the complete and incomplete fusions are
investigated by considering the $^8$Li+$^{208}$Pb reaction. By decreasing the
projectile ground-state binding energy $\varepsilon_b$ from its known
experimental value, the complete fusion is shown to have insignificant
dependence on such variations, whereas the incomplete fusion strongly depends
on that. The complete and incomplete fusion cross sections are calculated by
using a combination of both continuum-discretized coupled-channel and sum-rule
models. To this end, an incident-energy dependent cut-off angular momentum
$L_c$ is first obtained by using the available complete fusion experimental
data, within an approach which is extended to model results obtained for other
incident-energies. An approximated fitted expression linking $L_c$ to the
well-known critical value $L_{\rm crit}$ derived by Wilczy\'nski [Nucl. Phys. A
216 (1973) 386] suggests a generalization of the corresponding sum-rule model
to energies around and below the Coulomb barrier.
