Three-body approach to direct nuclear reactions involving weakly bound systems

The Faddeev type Alt, Grassberger and Sandhas (AGS) equations for transition operators were, in recent years, consistently applied to study direct nuclear reactions using realistic nucleon-nucleus optical potentials together with modern nucleon-nucleon interactions. The equations are solved numerically using momentum-space partial-wave basis. The Coulomb interaction between charged particles is included using a novel implementation of the screening and renormalization method. The AGS equations have been successfully used to study elastic, transfer, and breakup reactions in three-body-like nuclear systems. Examples are deuteron scattering on stable nuclei ${}^4$He, ${}^{10}$Be, ${}^{12}$C, ${}^{14}$C, ${}^{16}$O, ${}^{40}$Ca, and ${}^{58}$Ni and proton scattering on weakly bound two-body system such as ${}^{11}$Be, ${}^{13}$C, ${}^{15}$C, and ${}^{17}$O. These calculations allow to evaluate the accuracy of traditional approximate nuclear reaction approaches like the continuum-discretized coupled-channels (CDCC) method but also to test novel dynamical models such as energy dependent and nonlocal optical potentials.