Simultaneous optical model analysis of elastic scattering, fusion, and breakup for theBe9+Sm144system at near-barrier energies

Abstract

A simultaneous optical model calculation of elastic scattering, complete fusion, and breakup cross sections for energies around the Coulomb barrier is presented for reactions involving the weakly bound projectile $^{9}\mathrm{Be}$ on the medium size target $^{144}\mathrm{Sm}$. In the calculations, the nuclear polarization potential $U$ is split into a volume part ${U}_{F}$, which is responsible for fusion reactions, and a surface part ${U}_{\mathrm{DR}}$, which accounts for direct reactions. A simultaneous ${\ensuremath{\chi}}^{2}$ analysis of elastic and complete fusion data shows that the extracted optical potential parameters of the real ${V}_{F}$ and imaginary ${W}_{F}$ parts of ${U}_{F}$ and the corresponding parts ${V}_{\mathrm{DR}}$ and ${W}_{\mathrm{DR}}$ of ${U}_{\mathrm{DR}}$ satisfy separately the dispersion relation. Energy-dependent forms for the fusion and direct reaction potentials indicate that, at the strong absorption radius, the direct reaction potentials dominate over the fusion potentials$.$ Moreover, the imaginary direct reaction potential results in a rather smooth function of $E$ around the barrier energy. These findings show that the threshold anomaly, usually present in reactions with tightly bound projectiles, is not exhibited for the system $^{9}\mathrm{Be}+^{144}\mathrm{Sm}$. Within this formalism, the effect of breakup reactions on complete fusion is studied by turning on and off the potentials responsible for breakup reactions.