Values of the proton analysing power in the $pdto{}^{3}textrm{He},pi^0/^{3}textrm{H},pi^+$ reactions at 350-360~MeV per nucleon were obtained by using a polarised proton beam incident on a deuterium cluster-jet target and with a polarised deuteron beam incident on a target cell filled with polarised hydrogen. These results have a much larger angular coverage than existing data. First measurements are also presented of the deuteron vector analysing power and the deuteron-proton spin correlations. Data were also obtained on the deuteron-proton spin correlation and proton analysing power at small angles at 600~MeV per nucleon, though the angular coverage at this energy was much more restricted even when using a deuteron beam. By combining the extrapolated values of the spin correlations to the forward or backward directions with published measurements of the deuteron tensor analysing powers, the relative phases between the two non-vanishing amplitudes were evaluated.
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