Extended optical model analyses of elastic scattering and fusion cross sections for heavy-ion collisions with loosely bound projectiles at near-Coulomb-barrier energies

Abstract

Within the framework of an extended optical model, simultaneous ${\ensuremath{\chi}}^{2}$ analyses are performed for elastic scattering and fusion cross-section data for $^{9}\mathrm{Be}+^{209}\mathrm{Bi}$ and $^{6}\mathrm{Li}+^{208}\mathrm{Pb}$ systems, both involving loosely bound projectiles, at near-Coulomb-barrier energies to determine the polarization potential as decomposed into direct reaction $(\text{DR})$ and fusion parts. We show that both $\text{DR}$ and fusion potentials extracted from ${\ensuremath{\chi}}^{2}$ analyses separately satisfy the dispersion relation, and that the expected threshold anomaly appears in the fusion part. The $\text{DR}$ potential turns out to be a rather smooth function of the incident energy, and has a magnitude at the strong absorption radius much larger than the fusion potential, explaining why a threshold anomaly has not been seen in optical potentials deduced from fits to the elastic-scattering data without such a decomposition. Using the extracted $\text{DR}$ potential, we examine the effects of projectile breakup on fusion cross sections ${\ensuremath{\sigma}}_{F}$. The observed suppression of ${\ensuremath{\sigma}}_{F}$ in the above-barrier region can be explained in terms of the flux loss due to breakup. However, the observed enhancement of ${\ensuremath{\sigma}}_{F}$ in the subbarrier region cannot be understood in terms of the breakup effect. Rather, the enhancement can be related to the $Q$ value of the neutron transfer within the systems, supporting the ideas of Stelson et al. [Phys. Lett. B 205, 190 (1988); Stelson et al.Phys. Rev. C 41, 1584 (1990)] that subbarrier fusion starts to occur when the colliding ions are at a distance where the barrier against the flow of the valence neutrons disappears and thus neutron exchange can take place freely.