Abstract
The development of a continuum-bin scheme of discretization for three-body projectiles is necessary for studies of reactions of Borromean nuclei such as $^{6}\mathrm{He}$ within the continuum-discretized coupled-channels approach. Such a procedure, for constructing bin states on selected continuum energy intervals, is formulated and applied for the first time to reactions of a three-body projectile. The continuum representation uses the eigenchannel expansion of the three-body $S$ matrix. The method is applied to the challenging case of the $^{6}\mathrm{He}+^{208}\mathrm{Pb}$ reaction at 22 MeV, where an accurate treatment of both the Coulomb and the nuclear interactions with the target is necessary.
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