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An approach is proposed to calculate the direct reaction (DR) and fusionprobabilities for heavy ion collisions at near-Coulomb-barrier energies asfunctions of the distance of closest approach D within the framework of theoptical model that introduces two types of imaginary potentials, DR and fusion.The probabilities are calculated by using partial DR and fusion cross sections,together with the classical relations associated with the Coulomb trajectory.Such an approach makes it possible to analyze the data for angulardistributions of the inclusive DR cross section, facilitating the determinationof the radius parameters of the imaginary DR potential in a less ambiguousmanner. Simultaneous $\chi^{2}$-analyses are performed of relevant data for the$^{16}$O+$^{208}$Pb system near the Coulomb-barrier energy

Semiclassical character and optical model description of heavy ion scattering, direct reactions, and fusion at near-barrier energies