A set of differential cross section of the three-body $^{2}$H($d$,$dp$)$n$ breakup reaction at 160 MeV deuteron beam energy are presented for 147 kinematically complete configurations near the quasi-free scattering kinematics. The experiment was performed at KVI in Groningen, the Netherlands using the BINA detector. The cross-section data have been normalized to the $^{2}$H($d$,$d$)$^{2}$H elastic scattering cross section. The data are compared to the recent single-scattering approximation (SSA) calculations for three-cluster breakup in deuteron-deuteron collisions. Confronting the SSA predictions with the experimental data shows that SSA provides the correct order of magnitude of the cross-section data. The studied energy is probably too low to meet the SSA assumptions which prevents better accuracy of the description.
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