Proton-and neutron-rich breakups near zero binding energy

An analysis of the elastic scattering and breakup cross sections in the 17 F / 17 O + 208 Pb reactions in the zero binding energy limit, is presented. The main motivation was to investigate whether finite reaction observables can be obtained for a neutron-rich system in this limit, where it can be regarded as an open quantum system. It is first found that as the binding energy tends to zero, the ground-state wave function of the 17 O ( 16 O +n) system falls asymptotically as ∼ 1 / r ℓ b (where ℓ b = 2 , is the ground-state orbital angular momentum). For both projectiles, finite elastic scattering and breakup cross sections are obtained in the zero binding energy limit, where they also become insensitive to the variation of the binding energy. For the 17 F projectile, this is due to the core-proton Coulomb barrier, whereas for the 17 O projectile, it is due to the ∼ 1 / r ℓ b asymptotic behavior of the ground-state wave function in this limit. In conclusion, finite reaction observables in the breakup of an open quantum system can be obtained for ℓ b ≥ 2 .