Energy dependence of the optical potentials for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>9</mml:mn></mml:mmultiscripts></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mn>208</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>9</mml:mn></mml:mmultiscripts></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Bi</mml:mi><mml:mprescripts/><mml:none/><mml:mn>209</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>systems at near-Coulomb-barrier energies

We analyze the energy dependence of the interacting optical potential, at near barrier energies, for two systems involving the weakly bound projectile $^{9}\mathrm{Be}$ and the heavy $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ targets, by the simultaneous fit of elastic scattering angular distributions and fusion excitation functions. The approach used consists of dividing the optical potential into two parts. A short-range potential ${V}_{F}+i{W}_{F}$ that is responsible for fusion, and a superficial potential ${V}_{\mathrm{DR}}+i{W}_{\mathrm{DR}}$ for direct reactions. It is found, for both systems studied, that the fusion imaginary potential ${W}_{F}$ presents the usual threshold anomaly (TA) observed in tightly bound systems, whereas the direct reaction imaginary potential ${W}_{\mathrm{DR}}$ shows a breakup threshold anomaly (BTA) behavior. Both potentials satisfy the dispersion relation. The direct reaction polarization potential predominates over the fusion potential and so a net overall behavior is found to follow the BTA phenomenon.