Detailed determination of the nuclear fusion radius by a simultaneous optical model calculation of elastic scattering and fusion cross sections in reactions involving weakly bound projectiles

Abstract

Within the optical model for direct reactions, simultaneous calculations of elastic scattering, complete fusion, and total reaction cross sections for energies around the Coulomb barrier are presented for reactions involving the weakly bound projectile $^{9}\mathrm{Be}$ on $^{64}\mathrm{Zn}$. Volume (${W}_{F}$) and surface (${W}_{\mathrm{DR}}$) Woods-Saxon optical potentials are used such that the former is responsible only for complete fusion reactions while the latter for all direct reactions plus incomplete fusion. Simultaneous fits can be obtained with several sets of potential parameters, but if we impose the condition that the strength of ${W}_{F}$ is smaller than the strength of ${W}_{\mathrm{DR}}$ at the tail region of the potential (this condition is discussed in detail), then values are required for ${r}_{F}$ and ${r}_{\mathrm{DR}}$ of around $1.6$ and 1.7--1.9 fm, respectively. These values are much larger than those frequently used in barrier penetration model calculations. Through the energy dependence of the real and imaginary parts of the polarization potentials, we show that the usual threshold anomaly does not show up for this system, but instead there is evidence of the presence of a breakup threshold anomaly.