Momentum Space Faddeev Calculation of $d+\alpha$ Scattering

The ($d$,$p$) reaction constitutes an important tool for extracting nuclear structure information and contributes to the understanding of the dynamics of reactions. For the three body system $n+p+A$, it is advantageous to treat the problem within a Faddeev framework. Here we present phase shifts and angular distributions for $d+\alpha$ elastic scattering below and above the three-body breakup threshold and reaction cross sections up to 30~MeV deuteron kinetic energy and benchmark with calculations in the literature. We will also study the very low energy behavior below the three-body breakup threshold. The interactions in the subsystems are given by multi-rank separable representations based on the Ernst-Shakin-Thaler scheme of the CD-Bonn interaction for the $np$ system and Woods-Saxon forms for the neutron(proton)-$\alpha$ potential, which already are successfully applied in calculating the ground state of $^6$Li\footnote{L. Hlophe, Jin Lei, Ch. Elster, A. Nogga, F.M. Nunes, Phys. Rev. C{\bf 96}, 064003 (2017)}. For the initial work the Coulomb interaction is omitted. However, we note that for taking Coulomb into account without screening, separable interaction must be used in the subsystems. Thus, a careful benchmarking of our approach for scattering is warrented.