The 11Li + p and 11Li + d reactions are investigated in the Continuum Discretized Coupled Channel (CDCC) method with a three-body description (9Li + n + n) of 11Li. I first discuss the properties of 11Li, and focus on E1 transition probabilities to the continuum. The existence of a 1- resonance at low excitation energies is confirmed, but the associated E1 transition from the ground state does not have an isoscalar character, as suggested in a recent experiment. In a second step, I study the 11Li + p elastic cross section at Elab = 66 MeV in the CDCC framework. I obtain a fair agreement with experiment, and show that breakup effects are maximal at large angles. The breakup cross section is shown to be dominated by the 1- dipole state in 11Li, but the role of this resonance is minor in elastic scattering. From CDCC equivalent 11Li + p and 11Li + n potentials, I explore the 11Li + d cross section within a standard three-body 11Li +(p + n) model. At small angles, the experimental cross section is close to the Rutherford scattering cross section, which is not supported by the CDCC. A five-body (9Li+n+n)+(p+n) is then performed. Including breakup states in 11Li and in the deuteron represents a numerical challenge for theory, owing to the large number of channels. Although a full convergence could not be reached, the CDCC model tends to overestimate the data at small angles. I suggest that measurements of the 9Li + p elastic scattering would be helpful to determine more accurate optical potentials. The current disagreement between experiment and theory on 11Li + d scattering also deserves new experiments at other energies.
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