Testing the continuum discretized coupled channel method for deuteron induced reactions

The Continuum Discretized Coupled Channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the 3-body problem can be solved exactly within the Faddeev formalism which explicitly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact 3-body Faddeev formulation, we study deuteron induced reactions on: i) $^{10}$Be at $E_{\rm d}= 21.4, 40.9 \; {\rm and} \; 71$ MeV; ii) $^{12}$C at $E_{\rm d} = 12 \; {\rm and} \; 56$ MeV; and iii) $^{48}$Ca at $E_{\rm d} = 56$ MeV. We calculate elastic, transfer and breakup cross sections. Overall, the discrepancies found for elastic scattering are small with the exception of very backward angles. For transfer cross sections at low energy $\sim$10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. On the contrary, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here.