Differential cross sections of $^{2}$H(d, d)d elastic scattering and proton transfer $^{2}$H(d, $^{3}$He)n reactions at 160 MeV beam energy have been obtained. They have been normalized relative to the existing cross-section data for the $^{2}$H(d, d)d elastic scattering at 180 and 130 MeV, benefiting from the negligible energy dependence of this observable at certain range of the four momentum transfer. The experiment was performed at KVI in Groningen, the Netherlands using the BINA detector. The elastic scattering data are compared to theoretical predictions based on the lowest-order term in the Neumann series expansion for four-nucleon transition operators. The calculations underpredict the data. The data presented in this paper can be used to validate the future theoretical findings.
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