We present a new reaction model, which permits the description of reactions where both colliding nuclei present a low threshold to breakup. The method corresponds to a four-body extension of the Continuum Discretized Coupled Channel (CDCC) model. We first discuss the theoretical formalism, and then apply the method to 11Be+d scattering at Ecm = 45.5 MeV. The 11Be nucleus and the deuteron are described by 10Be+n and p + n structures, respectively. The model involves very large bases, but we show that an accurate description of elastic-scattering data may be achieved only when continuum states of 11Be and of the deuteron are introduced simultaneously. We also discuss breakup calculations, and show that the cross section is larger for 11Be than for the deuteron. The present theory provides reliable wave functions that may be used in the analysis of (d,p) or (d,n) experiments involving radioactive beams.
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